[1] C., Ané, S., Blachère, D., Chafai, P., Fougères, I., Gentil, F., Malrieu, C., Roberto and G., Scheffer, Sur les inégalités de Sobolev logarithmiques, Panoramas and Synthèses 10, Sociéteé Mathématique de France, Paris, 2000.Google Scholar

[2] W., Arveson, A short course on spectral theory, Graduate Texts in Mathematics 209, Springer, New York, 2002.Google Scholar

[3] R., Bañuelos and C., Moore, Probabilistic behavior of harmonic functions, Birkhäuser, Basel, 1999.Google Scholar

[4] B., Beauzamy, Introduction to Banach spaces and their geometry, North-Holland, Amsterdam, 1985.Google Scholar

[5] Y., Benyamini and J., Lindenstrauss, Geometric nonlinear functional analysis, Vol. 1, American Mathematical Society, Providence, RI, 2000.Google Scholar

[6] J., Bergh and J., Löfström, Interpolation spaces: an introduction, Springer, Berlin, 1976.Google Scholar

[7] C., Bennett and R., Sharpley, Interpolation of operators, Academic Press, Boston, 1988.Google Scholar

[8] J., Bourgain, La propriété de Radon-Nikodym, Publications mathématiques de l'Université Pierre et Marie Curie, 36 (1979).Google Scholar

[9] J., Bourgain, New classes of Lp-spaces, Lecture Notes in Mathématics 889, Springer, Berlin, 1981.Google Scholar

[10] R., Bourgin, Geometric aspects of convex sets with the Radon-Nikodým property, Lecture Notes in Mathematics 993, Springer, Berlin, 1983.Google Scholar

[11] L., Breiman, Probability, corrected reprint of the 1968 original Classics in applied mathematics, vol. 7, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1992.Google Scholar

[12] Yu. A., Brudnyi and N. Ya., Krugljak, Interpolation functors and interpolation spaces, Vol. I, North-Holland, Amsterdam, 1991.Google Scholar

[13] M., Bruneau, Variation totale d'une fonction, Lecture Notes in Mathematics 413, Springer, New York, 1974.Google Scholar

[14] D. L., Burkholder, Selected works of Donald L. Burkholder, edited by Burgess, Davis and Renming, Song, Springer, New York, 2011.Google Scholar

[15] C., Carathéodory, Conformal representation, 2nd ed., Cambridge University Press, New York, 1952.Google Scholar

[16] G., Choquet, Lectures on analysis, Vol. II: Representation Theory, Benjamin, New York, 1969.Google Scholar

[17] I., Cuculescu and A. G., Oprea, Non-commutative probability, Kluwer, New York, 1994.Google Scholar

[18] C., Dellacherie and P. A., Meyer, Probabilities and potential. B. Theory of martingales, North-Holland, Amsterdam, 1982.Google Scholar

[19] R., Deville, G., Godefroy and V., Zizler, Smoothness and renormings in Banach spaces, PitmanMonographs and Surveys in Pure and Applied Mathematics 64, John Wiley, New York, 1993.Google Scholar

[20] J., Diestel, Geometry of Banach spaces – Selected topics, Springer Lecture Notes 485, Springer, New York, 1975.Google Scholar

[21] J., Diestel and J. J., Uhl Jr., Vector measures, Mathematical Surveys 15, American Mathematical Society, Providence, 1977.Google Scholar

[22] J. L., Doob, Stochastic processes, reprint of the 1953 original, Wiley Classics Library, Wiley-Interscience, New York, 1990.Google Scholar

[23] R., Dudley and R., Norvaiša, Differentiability of six operators on nonsmooth functions and p-variation, with the collaboration of Jinghua Qian, Lecture Notes in Mathematics 1703, Springer, Berlin, 1999.Google Scholar

[24] R., Dudley and R., Norvaiša, Concrete functional calculus, Springer Monographs in Mathematics, Springer, New York, 2011.Google Scholar

[25] P., Duren, Theory of Hp spaces, Academic Press, New York, 1970.Google Scholar

[26] R., Durrett, Brownian motion and martingales in analysis, Wadsworth Mathematics Series, Wadsworth, Belmont, CA, 1984.Google Scholar

[27] R., Durrett, Probability: theory and examples, 4th ed., Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 2010.Google Scholar

[28] H., Dym and H. P., McKean, Fourier series and integrals, Academic Press, New York, 1972.Google Scholar

[29] G. A., Edgar and L., Sucheston, Stopping times and directed processes, Cambridge University Press, Cambridge, 1992.Google Scholar

[30] R. E., Edwards and G. I., Gaudry, Littlewood–Paley and multiplier theory, Springer, New York, 1977.Google Scholar

[31] E., Effros and Z. J., Ruan, Operator spaces, Oxford University Press, Oxford, 2000.Google Scholar

[32] J., García-Cuerva and J. L, Rubio de Francia, Weighted norm inequalities and related topics, North-Holland, Amsterdam, 1985.Google Scholar

[33] J., Garnett, Bounded analytic functions, Academic Press, New York, 1981.Google Scholar

[34] A. M., Garsia, Martingale inequalities: seminar notes on recent progress,Mathematics Lecture Notes Series, W. A. Benjamin, Reading, MA, 1973.Google Scholar

[35] I., Gikhman and A., Skorokhod, The theory of stochastic processes, III, reprint of the 1974 edition, Springer, Berlin, 2007.Google Scholar

[36] L., Grafakos, Classical Fourier analysis, Springer, New York, 2008.Google Scholar

[37] L., Grafakos, Modern Fourier analysis, Springer, New York, 2009.Google Scholar

[38] P., Hàjek, S. Montesinos, Santalucša, J., Vanderwerff and V., Zizler, Biorthogonal systems in Banach spaces, CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC 26, Springer, New York, 2008.Google Scholar

[39] H., Helson, Lectures on invariant subspaces, Academic Press, New York, 1964.Google Scholar

[40] K., Hoffman, Banach spaces of analytic functions, Prentice Hall, Englewood Cliffs, NJ, 1962.Google Scholar

[41] L., Hörmander, An introduction to complex analysis in several variables, Van Nostrand, Princeton, NJ, 1966.Google Scholar

[42] L., Hörmander, Notions of convexity, Birkhäuser, Boston, 1994.Google Scholar

[43] R., Kadison and J., Ringrose, Fundamentals of the theory of operator algebras, Vol. II, Advanced theory, Academic Press, New York, 1986.Google Scholar

[44] J. P., Kahane, Some random series of functions, 2nd ed., Cambridge Studies in Advanced Mathematics 5, Cambridge University Press, Cambridge, 1985.Google Scholar

[45] N., Kalton, N., Peck and J., Roberts, An F-space sampler, London Mathematical Society Lecture Note Series 89, Cambridge University Press, Cambridge, 1984.Google Scholar

[46] B., Kashin and A., Saakyan, Orthogonal series, Translations of Mathematical Monographs 75, American Mathematical Society, Providence, RI, 1989.Google Scholar

[47] T., Kato, Perturbation theory for linear operators, reprint of the 1980 edition, Classics in Mathematics, Springer, Berlin, 1995.Google Scholar

[48] Y., Katznelson, An introduction to harmonic analysis, 3rd ed., Cambridge University Press, Cambridge, 2004.Google Scholar

[49] P., Koosis, Introduction to Hp-spaces, 2nd ed., Cambridge University Press, Cambridge, 1998.Google Scholar

[50] O., Kouba and A., Pallarès, Groupe de travail sur les espaces de Banach (B. Maurey et G. Pisier, 1986-1987), handwritten lecture notes.

[51] S. G., Krein, Yu., Petunin and E. M., Semenov, Interpolation of linear operators, Translations of Mathematical Monographs 54, American Mathematical Society, Providence, RI, 1982.Google Scholar

[52] S., Kwapień and W., Woyczyński, Random series and stochastic integrals: single and multiple, Birkhäuser, Boston, 1992.Google Scholar

[53] M., Ledoux, The concentration of measure phenomenon, Mathematical Surveys and Monographs 89, American Mathematical Society, Providence, RI, 2001.Google Scholar

[54] M., Ledoux and M., Talagrand, Probability in Banach Spaces: isoperimetry and processes, Springer, Berlin, 1991.Google Scholar

[55] Le, Gall, Mouvement brownien, martingales et calcul stochastique, Springer, Heidelberg, 2013.Google Scholar

[56] D., Li and H., Queffélec, Introduction. l'étude des espaces de Banach, Analyse et probabilités, Société Mathématique de France, Paris, 2004.Google Scholar

[57] J., Lindenstrauss and L., Tzafriri. Classical Banach spaces II, Springer, New York, 1979.Google Scholar

[58] R., Long, Martingale spaces and inequalities, Peking University Press, Beijing, 1993.Google Scholar

[59] V., Mandrekar and B., Rüdiger, Stochastic integration in Banach spaces, Springer, New York, 2015.Google Scholar

[60] M., Marcus and G., Pisier, Random Fourier series with applications to harmonic analysis, Princeton University Press, Princeton, NJ, 1981.Google Scholar

[61] M., Métivier, Semimartingales: a course on stochastic processes, Walter de Gruyter, Berlin, 1982.Google Scholar

[62] M., Métivier and J., Pellaumail, Stochastic integration, Probability and Mathematical Statistics, Academic Press, New York, 1980.Google Scholar

[63] P. A., Meyer, Probabilités et potentiel, Hermann, Paris, 1966.Google Scholar

[64] P. A., Meyer, Un cours sur les intégrales stochastiques, Séminaire de Probabilités 10, Lecture Notes in Mathematics 511, Springer, Berlin, 1976.Google Scholar

[65] P. A., Meyer, Quantum probability for probabilists, Lecture Notes in Mathematics 1538, Springer, Berlin, 1993.Google Scholar

[66] P., Meyer-Nieberg, Banach lattices, Springer, Berlin, 1991.Google Scholar

[67] H. P., McKean Jr., Stochastic integrals, Academic Press, New York, 1969.Google Scholar

[68] V., Milman and G., Schechtman, Asymptotic theory of finite-dimensional normed spaces, with an appendix by M., Gromov, Lecture Notes in Mathematics 1200, Springer, Berlin, 1986.Google Scholar

[69] P., Mörters and Y., Peres, Brownian motion, with an appendix by Oded, Schramm and Wendelin, Werner, Cambridge University Press, Cambridge, 2010.Google Scholar

[70] P. F. X., Müller, Isomorphisms between H1 spaces,Monografie Matematyczne (New Series) 66, Birkhäuser, Basel, 2005.Google Scholar

[71] J., Neveu, Discrete-parameter Martingales, translated from the French by T. P., Speed, rev. ed., North-Holland Mathematical Library 10, North-Holland, Amsterdam, 1975.Google Scholar

[72] A., Osękowski, Sharp martingale and semimartingale inequalities, Birkhäuser/Springer, Basel, 2012.Google Scholar

[73] M. I., Ostrovskii, Metric embeddings, Bilipschitz and coarse embeddings into Banach spaces, De Gruyter, Berlin, 2013.Google Scholar

[74] K. R., Parthasarathy, An introduction to quantum stochastic calculus, Monographs in Mathematics, Birkhäuser, Basel, 1992.Google Scholar

[75] M. C., Pereyra and L., Ward, Harmonic analysis: from Fourier to wavelets, Institute for Advanced Study (IAS), Princeton, NJ, 2012.Google Scholar

[76] K., Petersen, Brownian motion, Hardy spaces, and bounded mean oscillation, Cambridge University Press, Cambridge, 1977.Google Scholar

[77] R. R., Phelps, Convex functions, monotone operators and differentiability, 2nd ed., Lecture Notes in Mathematics 1364, Springer, Berlin, 1993.Google Scholar

[78] A., Pietsch, Operator ideals, North-Holland, Amsterdam, 1980.Google Scholar

[79] G., Pisier, The volume of convex bodies and Banach space geometry, Cambridge University Press, Cambridge, 1989.Google Scholar

[80] G., Pisier, Introduction to operator space theory, London Mathematical Society Lecture Note Series 294, Cambridge University Press, Cambridge, 2003.Google Scholar

[81] D., Revuz and M., Yor, Continuous martingales and Brownian motion, 3rd ed., Springer, Berlin, 1999.Google Scholar

[82] A. W., Roberts and D. E., Varberg, Convex functions, Pure and Applied Mathematics 57, Academic Press, New York, 1973.Google Scholar

[83] L. C. G., Rogers and D., Williams, Diffusions, Markov processes, and martingales, Vol. 2, Itô calculus, Cambridge University Press, Cambridge, 2000.Google Scholar

[84] W., Rudin, Fourier analysis on groups, Interscience, New York, 1962.Google Scholar

[85] E. M., Stein, Topics in harmonic analysis related to the Littlewood–Paley theory, Annals of Mathematics Studies 63, Princeton University Press, Princeton, NJ, 1970.Google Scholar

[86] E., Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton University Press, Princeton, NJ, 1993.Google Scholar

[87] E., Stein and R., Shakarchi, Fourier analysis: an introduction, Princeton University Press, Princeton, NJ, 2003.Google Scholar

[88] E., Stein and R., Shakarchi, Complex analysis, Princeton University Press, Princeton, NJ, 2003.Google Scholar

[89] E., Stein and G., Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, NJ, 1971.Google Scholar

[90] D. W., Stroock, Probability theory: an analytic view, Cambridge University Press, Cambridge, 1993.Google Scholar

[91] M., Takesaki, Theory of operator algebras I, Springer, New York, 1979.Google Scholar

[92] M., Talagrand, The generic chaining: upper and lower bounds of stochastic processes, Springer Monographs in Mathematics, Springer, Berlin, 2005.Google Scholar

[93] A. E., Taylor, Introduction to functional analysis, John Wiley, New York, 1958.Google Scholar

[94] A. E., Taylor and D. C., Lay, Introduction to functional analysis, 2nd ed., John Wiley, New York, 1980.Google Scholar

[95] H., Triebel, Interpolation theory, function spaces, differential operators, 2nd ed., Johann Ambrosius Barth, Heidelberg, 1995.Google Scholar

[96] D., Voiculescu, K., Dykema and A., Nica, Free random variables, CRM Monograph Series 1, American Mathematical Society, Providence, RI, 1992.Google Scholar

[97] F., Weisz, MartingaleHardy spaces and their applications in Fourier analysis, Lecture Notes in Mathematics 1568, Springer, Berlin, 1994.Google Scholar

[98] P., Wojtaszczyk, A mathematical introduction to wavelets, London Mathematical Society Student Texts 37, Cambridge University Press, Cambridge, 1997.

[99] A., Zygmund, Trigonometric series, Vols. I and II, 3rd ed., Cambridge University Press, Cambridge, 2002.Google Scholar

[100] D., Aldous, Unconditional bases and martingales in Lp(F), Math. Proc. Cambridge Philos. Soc. 85 (1979), 117–123.Google Scholar

[101] M. E., Andersson, On the vector valued Hausdorff-Young inequality, Ark. Mat. 36 (1998), 1–30.Google Scholar

[102] T., Ando, Contractive projections in Lp-spaces, Pacific J. Math. 17 (1966), 391–405.Google Scholar

[103] N. H., Asmar, B. P., Kelly and S., Montgomery-Smith, A note on UMD spaces and transference in vector-valued function spaces, Proc. Edinburgh Math. Soc. (2) 39 (1996), 485–490.Google Scholar

[104] V., Aurich, Bounded holomorphic embeddings of the unit disk into Banach spaces, Manuscripta Math. 45 (1983), 61–67.Google Scholar

[105] V., Aurich, Bounded analytic sets in Banach spaces, Ann. Inst. Fourier (Grenoble) 36 (1986), 229–243.Google Scholar

[106] K., Azuma, Weighted sums of certain dependent random variables, Tôhoku Math. J. 19 (1967), 357–367.Google Scholar

[107] D., Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes, in Lectures on probability theory (Saint-Flour, 1992), Lecture Notes in Mathematics 1581, Springer, Berlin, 1994, 1–114.Google Scholar

[108] K., Ball, Markov, chains, Riesz transforms and Lipschitz maps, Geom. Funct. Anal. 2 (1992), 137–172.Google Scholar

[109] K., Ball, E., Carlen and E. H., Lieb, Sharp uniform convexity and smoothness inequalities for trace norms, Invent. Math. 115 (1994), 463–482.Google Scholar

[110] J., Bastero and M., Romance, Random vectors satisfying Khinchine-Kahane type inequalities for linear and quadratic forms, Math. Nach. 278 (2005), 1015–1024.Google Scholar

[111] F., Baudier, Metrical characterization of super-reflexivity and linear type of Banach spaces, Arch. Math. (Basel) 89 (2007), 419–429.Google Scholar

[112] F., Baudier and G., Lancien, Embeddings of locally finite metric spaces into Banach spaces, Proc. Am. Math. Soc. 136 (2008), 1029–1033.Google Scholar

[113] F., Baudier and S., Zhang, (β)-distortion of some infinite graphs, J. London Math. Soc., forthcoming.

[114] A., Beck, A convexity condition in Banach spaces and the strong law of large numbers, Proc. Am. Math. Soc. 13 (1962), 329–334.Google Scholar

[115] W., Beckner, Inequalities in Fourier analysis, Ann. Math. 102 (1975), 159–182.Google Scholar

[116] A., Benedek, A., Calderón and R., Panzone, Convolution operators on Banach space valued functions, Proc. Natl. Acad. Sci. USA 48 (1962), 356–365.Google Scholar

[117] J., Bergh, On the relation between the two complex methods of interpolation, Indiana Univ. Math. J. 28 (1979), 775–778.Google Scholar

[118] J., Bergh and J., Peetre, On the spaces Vp(0 < p ≤ ∞), Boll. Un. Mat. Ital. 10 (1974), 632–648.Google Scholar

[119] E., Berkson, T. A., Gillespie and P. S., Muhly, Abstract spectral decompositions guaranteed by the Hilbert transform, Proc. London Math. Soc. 53 (1986), 489–517.Google Scholar

[120] A., Bernal and J., Cerdà, Complex interpolation of quasi-Banach spaces with an A-convex containing space, Ark. Mat. 29 (1991), 183–201.Google Scholar

[121] A., Bernard and B., Maisonneuve, Décomposition atomique de martingales de la classe H1, in Séminaire de Probabilités, Vol. XI, Lecture Notes in Mathematics 581, Springer, Berlin, 1977, 303–326.Google Scholar

[122] P., Biane and R., Speicher, Stochastic calculus with respect to free Brownian motion and analysis on Wigner space, Probab. Theory Related Fields 112 (1998), 373–409.Google Scholar

[123] O., Blasco, Hardy spaces of vector-valued functions: duality, Trans. Am. Math. Soc. 308 (1988), 495–507.Google Scholar

[124] O., Blasco and A., Pełczyński, Theorems of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces, Trans. Am. Math. Soc. 323 (1991), 335–367.Google Scholar

[125] O., Blasco and S., Pott, Operator-valued dyadic BMO spaces, J. Operator Theory 63 (2010), 333–347.Google Scholar

[126] G., Blower, A multiplier characterization of analytic UMD spaces, Studia Math. 96 (1990), 117–124.Google Scholar

[127] G., Blower and T., Ransford, Complex uniform convexity and Riesz measures, Can. J. Math. 56 (2004), 225–245.Google Scholar

[128] A., Bonami, Étude des coefficients de Fourier des fonctions de Lp (G), Ann. Inst. Fourier (Grenoble) 20 (1970), 335–402.

[129] A., Bonami and D., Lépingle, Fonction maximale et variation quadratique des martingales en présence d'un poids, Séminaire de Probabilités, Vol. XIII, Lecture Notes in Mathematics 721, Springer, Berlin, 1979, 294–306.Google Scholar

[130] J., Bourgain, A nondentable set without the tree property, Studia Math. 68 (1980), 131–139.Google Scholar

[131] J., Bourgain, New Banach space properties of the disc algebra and H∞, Acta Math. 152 (1984), 1–48.Google Scholar

[132] J., Bourgain, On trigonometric series in super reflexive spaces, J. London Math. Soc. 24 (1981), 165–174.Google Scholar

[133] J., Bourgain, A Hausdorff-Young inequality for B-convex Banach spaces, Pacific J. Math. 101 (1982), 255–262.Google Scholar

[134] J., Bourgain, Some remarks on Banach spaces in which martingale difference sequences are unconditional, Ark. Mat. 21 (1983), 163–168.Google Scholar

[135] J., Bourgain, On martingales transforms in finite-dimensional lattices with an appendix on the K-convexity constant, Math. Nachr. 119 (1984), 41–53.Google Scholar

[136] J., Bourgain, Extension of a result of Benedek, Calderón and Panzone, Ark. Mat. 22 (1984), 91–95.Google Scholar

[137] J., Bourgain, Vector valued singular integrals and the H1-BMO duality, in Probability theory and harmonic analysis, edited by Chao–Woyczynski, , Dekker, New York, 1986, 1–19.Google Scholar

[138] J., Bourgain, The metrical interpretation of superreflexivity in Banach spaces, Israel J. Math. 56 (1986), 222–230.Google Scholar

[139] J., Bourgain, Pointwise ergodic theorems for arithmetic sets (Appendix: The return time theorem), Publ. Math. Inst. Hautes Étud. Sci. 69 (1989), 5–45.Google Scholar

[140] J., Bourgain, On the radial variation of bounded analytic functions on the disc, Duke Math. J. 69 (1993), 671–682.Google Scholar

[141] J., Bourgain and W. J., Davis, Martingale transforms and complex uniform convexity, Trans. Am. Math. Soc. 294 (1986), 501–515.Google Scholar

[142] J., Bourgain and M., Lewko, Sidonicity and variants of Kaczmarz's problem, preprint, Arxiv, April 2015.

[143] J., Bourgain and H. P., Rosenthal, Martingales valued in certain subspaces of L1, Israel J. Math. 37 (1980), 54–75.

[144] J., Bourgain and H. P., Rosenthal, Applications of the theory of semi-embeddings to Banach space theory, J. Funct. Anal. 52 (1983), 149–188.Google Scholar

[145] J., Bourgain, H. P., Rosenthal and G., Schechtman, An ordinal Lp-index for Banach spaces, with application to complemented subspaces of Lp, Ann. Math. 114 (1981), 193–228.Google Scholar

[146] J., Bretagnolle, p-variation de fonctions aléatoires, I and II, in Séminaire de Probabilités, Vol. VI, Lecture Notes in Mathematics 258, Springer, Berlin, 1972, 51–71.Google Scholar

[147] J., Briët, A., Naor and O., Regev, Locally decodable codes and the failure of cotype for projective tensor products, Elect. Res. Announ. Math. Sci. 19 (2012), 120–130.Google Scholar

[148] J., Brossard, Comportement non-tangentiel et comportement brownien des fonctions harmoniques dans un demi-espace, Démonstration probabiliste d'un théorème de Calderón et Stein, Sém. Probab. (Strasbourg) 12 (1978), 378–397.Google Scholar

[149] A., Brunel and L., Sucheston, On J-convexity and some ergodic super-properties of Banach spaces, Trans. Am. Math. Soc. 204 (1975), 79–90.Google Scholar

[150] Q., Bu and P., Dowling, Observations about the projective tensor product of Banach spaces, III, Lp[0, 1] X, 1 < p < ∞, Quaest. Math. 25 (2002), 303–310.Google Scholar

[151] S., Bu, Deux remarques sur la propriété de Radon-Nikodym analytique, Ann. Fac. Sci. Toulouse 60 (1990), 79–89.Google Scholar

[152] S., Bu, Existence of radial limits of harmonic functions in Banach spaces, Chin. Ann. Math. Ser. B 13 (1992), 110–117. (Chinese summary in Chin. Ann. Math. Ser. A 13 (1992), 133.)Google Scholar

[153] S., Bu, On the analytic Radon-Nikodym property for bounded subsets in Banach spaces, J. London Math. Soc. 47 (1993), 484–496.Google Scholar

[154] S., Bu, A J-convex subset which is not PSH-convex, Acta Math. Sci. (English Ed.) 14 (1994), 446–450.Google Scholar

[155] S., Bu, A new characterization of the analytic Radon-Nikodym property for bounded subsets (English summary), Northeast. Math. J. 12 (1996), 227–229.Google Scholar

[156] S., Bu, The analytic Krein-Milman property in Banach spaces, Acta Math. Sci. (English Ed.) 18 (1998), 17–24.Google Scholar

[157] S., Bu, The existence of Jensen boundary points in complex Banach spaces, Syst. Sci. Math. Sci. 12 (1999), 8–12.Google Scholar

[158] S., Bu, A new characterisation of the analytic Radon-Nikodym property, Proc. Am. Math. Soc. 128 (2000), 1017–1022.Google Scholar

[159] S., Bu, The existence of radial limits of analytic functions with values in Banach spaces, Chin. Ann. Math. Ser. B 22 (2001), 513–518.Google Scholar

[160] S., Bu and B., Khaoulani, Une caractérization de la propriété de Radon–Nikodym analytique pour les espaces isomorphes à leur carrés, Math. Ann. 288 (1990), 345–360.Google Scholar

[161] S., Bu and C. Le, Merdy, Hp-maximal regularity and operator valued multipliers on Hardy spaces, Can. J. Math. 59 (2007), 1207–1222.Google Scholar

[162] S., Bu and W., Schachermayer, Approximation of Jensen measures by image measures under holomorphic functions and applications, Trans. Am. Math. Soc. 331 (1992), 585–608.Google Scholar

[163] A. V., Bukhvalov and A. A., Danilevich, Boundary properties of analytic and harmonic functions with values in a Banach space (Russian), Mat. Zametki 31 (1982), 203–214. 317. (English translation in Math. Notes 31 (1982), 104–110.(1983).)Google Scholar

[164] D. L., Burkholder, Maximal inequalities as necessary conditions for almost everywhere convergence, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 3 (1964), 75–88.Google Scholar

[165] D. L., Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19–42.Google Scholar

[166] D. L., Burkholder, Brownian motion and the Hardy spaces Hp, in Aspects of contemporary complex analysis, Academic Press, London, 1980, 97–118.Google Scholar

[167] D. L., Burkholder, A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional, Ann. Probab. 9 (1981), 997–1011.Google Scholar

[168] D. L., Burkholder, Martingale transforms and the geometry of Banach spaces, in Probability in Banach spaces, III, Lecture Notes in Mathematics 860, Springer, Berlin, 1981, 35–50.Google Scholar

[169] D. L., Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach space-valued functions, in Conference on Harmonic Analysis in honor of Antoni Zygmund, Vols. I and II (Chicago, Ill., 1981), Wadsworth, Belmont, CA, 1983, 270–286.Google Scholar

[170] D. L., Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), 647–702.Google Scholar

[171] D. L., Burkholder, Martingales and Fourier analysis in Banach spaces, in Probability and analysis (Varenna, 1985), 61–108, Lecture Notes in Mathematics 1206, Springer, Berlin, 1986, 61–108.Google Scholar

[172] D. L., Burkholder, Sharp inequalities for martingales and stochastic integrals, Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987), Astérisque 157–158 (1988), 75–94.Google Scholar

[173] D. L., Burkholder, Explorations in martingale theory and its applications, in École d'Été de Probabilités de Saint-Flour XIX – 1989, Lecture Notes in Mathematics 1464, Springer, Berlin, 1991, 1–66.Google Scholar

[174] D. L., Burkholder, Martingales and singular integrals in Banach spaces, in Handbook of the geometry of Banach spaces, Vol. I, North-Holland, Amsterdam, 2001, 233–269.Google Scholar

[175] D. L., Burkholder and R. F., Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249–304.Google Scholar

[176] D. L., Burkholder, R. F., Gundy and M. L., Silverstein, A maximal function characterization of the class Hp, Trans. Am. Math. Soc. 157 (1971), 137–153.Google Scholar

[177] A. P., Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190.Google Scholar

[178] S. D., Chatterji, Martingale convergence and the Radon-Nikodým theorem in Banach spaces, Math. Scand. 22 (1968), 21–41.Google Scholar

[179] J., Cheeger and B., Kleiner, Characterization of the Radon-Nikodym property in terms of inverse limits, Astérisque 321 (2008), 129–138.Google Scholar

[180] J., Cheeger and B., Kleiner, Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon-Nikodým property, Geom. Funct. Anal. 19 (2009), 1017–1028.Google Scholar

[181] C. H., Chu, A note on scattered C*-algebras and the Radon-Nikodym property, J. London Math. Soc. 24 (1981), 533–536.Google Scholar

[182] F., Cobos and J., Peetre, Interpolation of compactness using Aronszajn-Gagliardo functors, Israel J. Math. 68 (1989), 220–240.Google Scholar

[183] R. R., Coifman, A real variable characterization of Hp, Studia Math. 51 (1974), 269–274.Google Scholar

[184] R. R., Coifman, M., Cwikel, R., Rochberg, Y., Sagher and G., Weiss, Complex interpolation for families of Banach spaces, in Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 2, Proc. Sympos. Pure Math. XXXV, American Mathematical Society, Providence, RI, 1979, 269–282.Google Scholar

[185] R. R., Coifman, R., Rochberg, G., Weiss, M., Cwikel and Y., Sagher, The complex method for interpolation of operators acting on families of Banach spaces, in Euclidean harmonic analysis (Proc. Sem., Univ. Maryland, College Park, Md., 1979), Lecture Notes in Mathematics 779, Springer, Berlin, 1980, 123–153.

[186] R. R., Coifman, M., Cwikel, R., Rochberg, Y., Sagher and G., Weiss, A theory of complex interpolation for families of Banach spaces, Adv. Math. 43 (1982), 203–229.Google Scholar

[187] R. R., Coifman and S., Semmes, Interpolation of Banach spaces, Perron processes, and Yang- Mills, Am. J. Math. 115 (1993), 243–278.Google Scholar

[188] J., Conde, A note on dyadic coverings and nondoubling Calderón-Zygmund theory, J. Math. Anal. Appl. 397 (2013), 785–790.Google Scholar

[189] A., Connes, Classification of injective factors: cases II1, II∞, IIIλ, λ ≠ 1, Ann. Math. 104 (1976), 73–115.Google Scholar

[190] M. G., Cowling, G. I., Gaudry and T., Qian, A note on martingales with respect to complex measures, Miniconference on Operators in Analysis (Sydney, 1989), Proc. Centre Math. Anal. Austral. Nat. Univ. 24 (1990), 10–27.Google Scholar

[191] D., Cox, The best constant in Burkholder's weak-L1 inequality for the martingale square function, Proc. Am. Math. Soc. 85 (1982), 427–433.Google Scholar

[192] I., Cuculescu, Martingales on von Neumann algebras, J. Multivariate Anal. 1 (1971), 17–27.Google Scholar

[193] M., Cwikel, On (Lp0 (A0), Lp1 (A1))θ, q, Proc. Am. Math. Soc. 44 (1974), 286–292.Google Scholar

[194] M., Cwikel, Complex interpolation spaces, a discrete definition and reiteration, Indiana Univ. Math. J. 27 (1978), 1005–1009.Google Scholar

[195] M., Cwikel, Lecture notes on duality and interpolation spaces, arxiv 2008.

[196] M., Cwikel and S., Janson, Interpolation of analytic families of operators, Studia Math. 79 (1984), 61–71.Google Scholar

[197] M., Cwikel and S., Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, Adv. Math. 66 (1987), 234–290.Google Scholar

[198] M., Cwikel, M., Milman and Y., Sagher, Complex interpolation of some quasi-Banach spaces, J. Funct. Anal. 65 (1986), 339–347.Google Scholar

[199] M., Daher, Une remarque sur la propriété de Radon-Nikodým, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), 269–271.Google Scholar

[200] A., Daniluk, Themaximum principle for holomorphic operator functions, Integral Equations Operator Theory 69 (2011), 365–372.Google Scholar

[201] B., Davis. On the integrability of the martingale square function, Israel J. Math. 8 (1970), 187–190.Google Scholar

[202] W. J., Davis, Moduli of complex convexity, in Geometry of Banach spaces (Strobl, 1989), Cambridge University Press, Cambridge, 1990, 65–69.Google Scholar

[203] W. J., Davis, T., Figiel, W. B., Johnson and A., Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311–327.Google Scholar

[204] W. J., Davis, D. J. H., Garling and N., Tomczak-Jaegermann, The complex convexity of quasinormed linear spaces, J. Funct. Anal. 55 (1984), 110–150.Google Scholar

[205] W. J., Davis, W. B., Johnson and J., Lindenstrauss, The ln1 problem and degrees of nonreflexivity, Studia Math. 55 (1976), 123–139.Google Scholar

[206] W. J., Davis and J., Lindenstrauss, The n1 problem and degrees of non-reflexivity, II, Studia Math. 58 (1976), 179–196.Google Scholar

[207] M. M., Day, Uniform convexity in factor and conjugate spaces, Ann. Math. 45 (1944), 375–385.Google Scholar

[208] M. M., Day, Some more uniformly convex spaces, Bull. Am. Math. Soc. 47 (1941), 504–507.Google Scholar

[209] C., Demeter, M., Lacey, T., Tao and C., Thiele, Breaking the duality in the return times theorem, Duke Math. J. 143 (2008), 281–355.Google Scholar

[210] S., Dilworth, Complex convexity and the geometry of Banach spaces, Math. Proc. Cambridge Philos. Soc. 99 (1986), 495–506.Google Scholar

[211] S., Dineen and R., Timoney, Complex geodesics on convex domains, in Progress in functional analysis (Peniscola, 1990), North-Holland, Amsterdam, 1992, 333–365.Google Scholar

[212] J., Ding, J., Lee and Y., Peres, Markov type and threshold embeddings, Geom. Funct. Anal. 23 (2013), 1207–1229.Google Scholar

[213] R., Douglas, Contractive projections on an L1-space, Pacific J. Math. 15 (1965), 443–462.Google Scholar

[214] P., Dowling and G., Edgar, Some characterizations of the analytic Radon-Nikodým property in Banach spaces, J. Funct. Anal. 80 (1988), 349–357.Google Scholar

[215] P., Dowling, Stability of Banach space properties in the projective tensor product, Quaest. Math. 27 (2004), 1–7.Google Scholar

[216] G., Edgar, A non-compact Choquet theorem, Proc. Am. Math. Soc. 49 (1975), 354–358.Google Scholar

[217] G., Edgar, Analytic martingale convergence, J. Funct. Anal. 69 (1986), 268–280.Google Scholar

[218] G., Edgar, Complex martingale convergence, in Banach spaces. Proceedings, 1984, Lecture Notes in Mathematics 1166, Springer, New York, 1985, 38–59.Google Scholar

[219] G., Edgar and R. F., Wheeler, Topological properties of Banach spaces, Pacific J. Math. 115 (1984), 317–350.Google Scholar

[220] P., Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J.Math. 13 (1972), 281–288.Google Scholar

[221] T., Fack and H., Kosaki, Generalized s-numbers of τ-measurable operators, Pacific J. Math. 123(1986), 269–300.Google Scholar

[222] C., Fefferman and E., Stein, Hp spaces of several variables, Acta Math. 129 (1972), 137–193.

[223] T., Figiel, On the moduli of convexity and smoothness, Studia Math. 56 (1976), 121–155.Google Scholar

[224] T., Figiel, Uniformly convex norms on Banach lattices, Studia Math. 68 (1980), 215–247.Google Scholar

[225] T., Figiel, Singular integral operators: a martingale approach, in Geometry of Banach spaces (Strobl, 1989), London Math. Soc. Lecture Note Ser. 158, Cambridge University Press, Cambridge, 1990, 95–110.

[226] T., Figiel, On equivalence of some bases to the Haar system in spaces of vector-valued functions, Bull. Polish Acad. Sci. Math. 36 (1988), 119–131.

[227] T., Figiel, J., Lindenstrauss and V., Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 139 (1977), 53–94.Google Scholar

[228] T., Figiel and G., Pisier, Séries aléatoires dans les espaces uniformément convexes ou uniformément lisses, C.R. Acad. Sci. Paris Sér. A 279 (1974), 611–614.Google Scholar

[229] R., Fortet and E., Mourier, Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach, Studia Math. 15 (1955), 62–79.Google Scholar

[230] J., García-Cuerva, K. S., Kazaryan, V. I., Kolyada and J. L., Torrea, The Hausdorff-Young inequality with vector-valued coefficients and applications, Russian Math. Surveys 53 (1998), 435–513.Google Scholar

[231] D. J. H., Garling, Convexity, smoothness and martingale inequalities, Israel J. Math. 29 (1978), 189–198.Google Scholar

[232] D. J. H., Garling, Brownian motion and UMD-spaces, in Probability and Banach spaces (Zaragoza, 1985), Lecture Notes in Mathematics 1221, Springer, Berlin, 1986, 36–49.Google Scholar

[233] D. J. H., Garling, On martingales with values in a complex Banach space, Math. Proc. Camb. Philos. Soc. 104 (1988), 399–406.Google Scholar

[234] D. J. H., Garling, Random martingale transform inequalities, in Probability in Banach spaces 6 (Sandbjerg, 1986), Progr. Probab. 20, Birkhauser Boston, Boston, 1990, 101–119.

[235] D. J. H., Garling and S., Montgomery-Smith, Complemented subspaces of spaces obtained by interpolation, J. London Math. Soc. 44 (1991), 503–513.Google Scholar

[236] J., Garnett and P., Jones, The distance in BMO to L∞, Ann. Math. 108 (1978), 373–393.Google Scholar

[237] J., Garnett and P., Jones, BMO from dyadic BMO, Pacific J. Math. 99 (1982), 351–371.Google Scholar

[238] S., Geiss, A counterexample concerning the relation between decoupling constants and UMD-constants, Trans. Am. Math. Soc. 351 (1999), 1355–1375.Google Scholar

[239] S., Geiss, Contraction principles for vector valued martingales with respect to random variables having exponential tail with exponent 2 < α < ∞, J. Theoret. Probab. 14 (2001), 39–59.Google Scholar

[240] S., Geiss, S., Montgomery-Smith and E., Saksman, On singular integral and martingale transforms, Trans. Am. Math. Soc. 362 (2010), 553–575.Google Scholar

[241] N., Ghoussoub, G., Godefroy, B., Maurey and W., Schachermayer, Some topological and geometrical structures in Banach spaces, Mem. Am. Math. Soc. 70 (1987), 120 pp.Google Scholar

[242] N., Ghoussoub andW. B., Johnson, Counterexamples to several problems on the factorization of bounded linear operators, Proc. Am. Math. Soc. 92 (1984), 233–238.Google Scholar

[243] N., Ghoussoub, J., Lindenstrauss and B., Maurey, Analytic martingales and plurisubharmonic barriers in complex Banach spaces, in Banach space theory (Iowa City, IA, 1987), Contemp. Math. 85, American Mathematical Society, Providence, RI, 1989, 111–130.Google Scholar

[244] N., Ghoussoub and B., Maurey, Counterexamples to several problems concerning Gδ-embeddings, Proc. Am. Math. Soc. 92 (1984), 409–412.Google Scholar

[245] N., Ghoussoub and B., Maurey, Gδ-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), 72–97.

[246] N., Ghoussoub and B., Maurey, The asymptotic-norming and the Radon–Nikodým properties are equivalent in separable Banach spaces, Proc. Am. Math. Soc. 94 (1985), 665–671.

[247] N., Ghoussoub and B., Maurey, Hδ -embedding in Hilbert space and optimization on Gδ -sets, Mem. Am. Math. Soc. 62 (1986), 101.

[248] N., Ghoussoub and B., Maurey, Gδ-embeddings in Hilbert space. II, J. Funct. Anal. 78 (1988), 271–305.Google Scholar

[249] N., Ghoussoub and B., Maurey, Plurisubharmonic martingales and barriers in complex quasi- Banach spaces, Ann. Inst. Fourier (Grenoble) 39 (1989), 1007–1060.Google Scholar

[250] N., Ghoussoub, B., Maurey andW., Schachermayer, A counterexample to a problem on points of continuity in Banach spaces, Proc. Am. Math. Soc. 99 (1987), 278–282.Google Scholar

[251] N., Ghoussoub, B., Maurey and W., Schachermayer, Pluriharmonically dentable complex Banach spaces, J. Reine Angew. Math. 402 (1989), 76–127.Google Scholar

[252] N., Ghoussoub, B., Maurey and W., Schachermayer, Geometrical implications of certain infinite-dimensional decompositions, Trans. Am. Math. Soc. 317 (1990), 541–584.Google Scholar

[253] T. A., Gillespie, S., Pott, S., Treil and A., Volberg, Logarithmic growth for matrix martingale transforms, J. London Math. Soc. 64 (2001), 624–636.Google Scholar

[254] J., Globevnik, On complex strict and uniform convexity, Proc. Am. Math. Soc. 47 (1975), 175–178.Google Scholar

[255] Y., Gordon and D. R., Lewis, Absolutely summing operators and local unconditional structures, Acta Math. 133 (1974), 27–48.Google Scholar

[256] O., Guedon, Kahane-Khinchine type inequalities for negative exponent, Mathematika 46 (1999), 165–173.Google Scholar

[257] R., Gundy, A decomposition for L1-bounded martingales, Ann. Math. Stat. 39 (1968), 134–138.Google Scholar

[258] R., Gundy and N., Varopoulos, A martingale that occurs in harmonic analysis, Ark. Mat. 14 (1976), 179–187.Google Scholar

[259] V. I., Gurarii and N. I., Gurarii, Bases in uniformly convex and uniformly smooth Banach spaces (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 210–215.Google Scholar

[260] U., Haagerup, The best constants in the Khintchine inequality, Studia Math. 70 (1981), 231–283.Google Scholar

[261] U., Haagerup and G., Pisier, Factorization of analytic functions with values in noncommutative L1-spaces and applications, Can. Math. J. 41 (1989), 882–906.Google Scholar

[262] O., Hanner, On the uniform convexity of Lp and p, Ark. Mat. 3 (1956), 239–244.Google Scholar

[263] C. S., Herz, Bounded mean oscillation and regulated martingales, Trans. Am. Math. Soc. 193 (1974), 199–215.Google Scholar

[264] C. S., Herz, Hp-spaces of martingales, 0 < p ≤ 1, Z.Wahrscheinlichkeitstheorie Verw. Gebiete 28 (1973/74), 189–205.Google Scholar

[265] J., Hoffmann-Jørgensen, Sums of independent Banach space valued random variables, Studia Math. 52 (1974), 159–186.Google Scholar

[266] G., Hong, M., Junge and J., Parcet, Algebraic Davis decomposition and asymmetric Doob inequalities, Comm. Math. Physics, forthcoming.

[267] R. E., Huff and P. D., Morris, Geometric characterizations of the Radon-Nikodym property in Banach spaces, Studia Math. 56 (1976), 157–164.Google Scholar

[268] T., Hytönen, The real-variable Hardy space and BMO, lecture notes of a course at the University of Helsinki, winter 2010, http://www.helsinki.fi/∼tpehyton/Hardy/hardy.pdf.

[269] T., Hytönen and M., Lacey, Pointwise convergence of vector-valued Fourier series, Math. Ann. 357 (2013), 1329–1361.Google Scholar

[270] T., Hytonen, M., Lacey and I., Parissis, A variation norm Carleson theorem for vector valued Walsh-Fourier series, Rev. Mat. Iberoam. 30 (2014), 979–1014.Google Scholar

[271] A. Ionescu, Tulcea and C. Ionescu, Tulcea, Abstract ergodic theorems, Trans. Am. Math. Soc. 107 (1963), 107–124.Google Scholar

[272] K., Itô and M., Nisio, On the convergence of sums of independent Banach space valued random variables, Osaka J. Math. 5 (1968), 35–48.Google Scholar

[273] N., Jain and D., Monrad, Gaussian measures in Bp, Ann. Probab. 11 (1983), 46–57.

[274] R. C., James, Bases and reflexivity of Banach spaces, Ann. Math. 52 (1950), 518–527.Google Scholar

[275] R. C., James, Uniformly non-square Banach spaces, Ann. Math. 80 (1964), 542–550.Google Scholar

[276] R. C., James, Weak compactness and reflexivity, Israel J. Math. 2 (1964), 101–119.Google Scholar

[277] R. C., James, Reflexivity and the sup of linear functionals, Israel J. Math. 13 (1972), 289–300.Google Scholar

[278] R. C., James, Some self-dual properties of normed linear spaces, in Symposium on Infinite- Dimensional Topology (Louisiana State Univ., Baton Rouge, LA, 1967), Annals of Mathematical Studies 69, Princeton University Press, Princeton, NJ, 1972, 159–175.Google Scholar

[279] R. C., James, Super-reflexive Banach spaces, Can. J. Math. 24 (1972), 896–904.Google Scholar

[280] R. C., James, Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409–419.Google Scholar

[281] R. C., James, A nonreflexive Banach space that is uniformly nonoctahedral, Israel J. Math. 18 (1974), 145–155.Google Scholar

[282] R. C., James, Nonreflexive spaces of type 2, Israel J. Math. 30 (1978), 1–13.Google Scholar

[283] R. C., James and J., Lindenstrauss, The octahedral problem for Banach spaces, in Proceedings of the Seminar on Random Series, Convex Sets and Geometry of Banach Spaces, Various Publ. Ser. 24, Mat. Inst., Aarhus University, Aarhus, 1975, 100–120.

[284] R. C., James and J. J., Schäffer, Super-reflexivity and the girth of spheres, Israel J. Math. 11 (1972), 398–404.Google Scholar

[285] S., Janson, Minimal and maximalmethods of interpolation, J. Funct. Anal. 44 (1981), 50–73.Google Scholar

[286] S., Janson, On hypercontractivity for multipliers on orthogonal polynomials, Ark. Mat. 21 (1983), 97–110.Google Scholar

[287] S., Janson, On complex hypercontractivity, J. Funct. Anal. 151 (1997), 270–280.Google Scholar

[288] S., Janson and P., Jones, Interpolation between Hp spaces: the complex method, J. Funct. Anal. 48 (1982), 58–80.Google Scholar

[289] W. B., Johnson and G., Schechtman, Diamond graphs and super-reflexivity, J. Topol. Anal. 1 (2009), 177–189.Google Scholar

[290] W. B., Johnson and L., Tzafriri, Some more Banach spaces which do not have local unconditional structure, Houston J. Math. 3 (1977), 55–60.Google Scholar

[291] R. L., Jones, J. M., Rosenblatt and M., Wierdl, Oscillation in ergodic theory: higher dimensional results, Israel J. Math. 135 (2003), 1–27.Google Scholar

[292] M., Junge, Doob's inequality for non-commutative martingales, J. Reine Angew. Math. 549 (2002), 149–190.Google Scholar

[293] M., Junge, Fubini's theorem for ultraproducts of noncommmutativeLp-spaces, Can. J. Math. 56 (2004), 983–1021.Google Scholar

[294] M., Junge and Q., Xu, On the best constants in some non-commutative martingale inequalities, Bull. London Math. Soc. 37 (2005), 243–253.Google Scholar

[295] M., Junge and Q., Xu, Noncommutative Burkholder/Rosenthal inequalities, Ann. Probab. 31 (2003), 948–995.Google Scholar

[296] M., Junge and Q., Xu, Noncommutative Burkholder/Rosenthal inequalities, II, Applications, Israel J. Math. 167 (2008), 227–282.Google Scholar

[297] M. I., Kadec and A., Pełczy'nski, Bases, lacunary sequences and complemented subspaces in the spaces Lp, Studia Math. 21 (1961/1962), 161–176.Google Scholar

[298] S., Kakutani, Markoff process and the Dirichlet problem, Proc. Jpn. Acad. 21 (1945), 227–233.Google Scholar

[299] N., Kalton, Differentials of complex interpolation processes for Köthe function spaces, Trans. Am. Math. Soc. 333 (1992), 479–529.Google Scholar

[300] N., Kalton, Lattice structures on Banach spaces, Mem. Am. Math. Soc. 103 (1993), 99 pp.Google Scholar

[301] N., Kalton, Complex interpolation of Hardy-type subspaces, Math. Nachr. 171 (1995), 227–258.Google Scholar

[302] N., Kalton, S. V., Konyagin and L., Vesely, Delta-semidefinite and delta-convex quadratic forms in Banach spaces, Positivity 12 (2008), 221–240.Google Scholar

[303] N., Kalton and S., Montgomery-Smith, Interpolation of Banach spaces, in Handbook of the geometry of Banach spaces, Vol. 2, North-Holland, Amsterdam, 2003, 1131–1175.

[304] N. H., Katz, Matrix valued paraproducts, J. Fourier Anal. Appl. 300 (1997), 913–921.Google Scholar

[305] S. V., Kisliakov, A remark on the space of functions of bounded p-variation, Math. Nachr. 119 (1984), 137–140.Google Scholar

[306] S. V., Kisliakov, Interpolation of Hp-spaces: some recent developments, in Function spaces, interpolation spaces, and related topics (Haifa, 1995), Israel Math. Conf. Proc. 13, Bar-Ilan University, Ramat Gan, 1999, 102–140.Google Scholar

[307] B., Kloeckner, Yet another short proof of the Bourgain's distortion estimate for embedding of trees into uniformly convex Banach spaces, Israel J. Math. 200 (2014), 419–422.Google Scholar

[308] H., Koch, Adapted function spaces for dispersive equations, in Singular phenomena and scaling in mathematical models, Springer, Cham, 2014, 49–67.Google Scholar

[309] H., Kosaki, Applications of the complex interpolation method to a von Neumann algebra: noncommutative Lp-spaces, J. Funct. Anal. 56 (1984), 29–78.Google Scholar

[310] H., Konig, On the Fourier-coefficients of vector-valued functions, Math. Nachr. 152 (1991), 215–227.Google Scholar

[311] O., Kouba, H1-projective spaces, Q. J. Math. Oxford Ser. 41 (1990), 295–312.Google Scholar

[312] J. L., Krivine, Sous-espaces de dimension finie des espaces de Banach reticules, Ann. Math. 104 (1976), 1–29.Google Scholar

[313] J. L., Krivine and B., Maurey, Espaces de Banach stables, Israel J. Math. 39 (1981), 273–295.Google Scholar

[314] K., Kunen and H. P., Rosenthal, Martingale proofs of some geometrical results in Banach space theory, Pacific J. Math. 100 (1982), 153–175.Google Scholar

[315] S., Kwapień, Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients, Studia Math. 44 (1972), 583–595.Google Scholar

[316] S., Kwapień, On operators factorizable through Lp space, Bull. Soc.Math. France (Mémoire) 31–32 (1972), 215–225.Google Scholar

[317] G., Lancien, On uniformly convex and uniformly Kadec-Klee renormings, Serdica Math. J. 21 (1995), 1–18.

[318] R., Latała and K., Oleszkiewicz, On the best constant in the Khinchin-Kahane inequality, Studia Math. 109 (1994), 101–104.Google Scholar

[319] J. M., Lee, Biconcave-function characterisations of UMD and Hilbert spaces, Bull. Austral. Math. Soc. 47 (1993), 297–306.Google Scholar

[320] J. M., Lee, On Burkholder's biconvex-function characterization of Hilbert spaces, Proc. Am. Math. Soc. 118 (1993), 555–559.Google Scholar

[321] J., Lee and A., Naor, Embedding the diamond graph in Lp and dimension reduction in L1, Geom. Funct. Anal. 14 (2004), 745–747.Google Scholar

[322] J. R., Lee, A., Naor, and Y., Peres, Trees andMarkov convexity, Geom. Funct. Anal. 18 (2009), 1609–1659. (Conference version in Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, 2006, 1028–1037.)Google Scholar

[323] K. de, Leeuw, On Lp multipliers, Ann. Math. 81 (1965), 364–379.Google Scholar

[324] C. Le, Merdy and Q., Xu, Strong q-variation inequalities for analytic semigroups, Ann. Inst. Fourier (Grenoble) 62 (2012), 2069–2097.Google Scholar

[325] E., Lenglart, D., Lépingle and M., Pratelli, Présentation unifiée de certaines inégalités de la théorie des martingales, with an appendix by Lenglart, in Seminar on Probability, XIV (Paris, 1978/1979), Lecture Notes in Mathematics 784, Springer-Verlag, Berlin, 1980, 26–52.

[326] D., Lépingle, Quelques inégalités concernant les martingales, StudiaMath. 59 (1976), 63–83.Google Scholar

[327] D., Lépingle, La variation d'ordre p des semi-martingales, Z.Wahrscheinlichkeitstheor. Verw. 36 (1976), 295–316.Google Scholar

[328] M., Lévy, L'espace d'interpolation réel (A0, A1)θ,p contient lp, C. R. Acad. Sci. Paris Sér.A-B 289 (1979), A675–A677.Google Scholar

[329] D. R., Lewis and C., Stegall, Banach spaces whose duals are isomorphic to l1 (Γ), J. Funct. Anal. 12 (1973), 177–187.Google Scholar

[330] J., Lindenstrauss, On the modulus of smoothness and divergent series in Banach spaces, Mich. Math. J. 10 (1963), 241–252.Google Scholar

[331] J., Lindenstrauss and A., Pełczy'nski, Absolutely summing operators in Lp-spaces and their applications, Studia Math. 29 (1968), 275–326.Google Scholar

[332] J., Lindenstrauss and H. P., Rosenthal, The Lp spaces, Israel J. Math. 7 (1969), 325–349.Google Scholar

[333] V. I., Liokumovich, Existence of B-spaces with a non-convex modulus of convexity, Izv. Vyssh. Uchebn. Zaved. Mat. 12 (1973), 43–49.Google Scholar

[334] J. L., Lions, Une construction d'espaces d'interpolation, C. R. Acad. Sci. Paris 251 (1960), 1853–1855.Google Scholar

[335] J. L., Lions and J., Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5–68.Google Scholar

[336] A. E., Litvak, Kahane-Khinchin's inequality for quasinorms, Can. Math. Bull. 43 (2000), 368–379.Google Scholar

[337] A., Lubin, Extensions of measures and the von Neumann selection theorem, Proc. Am. Math. Soc. 43 (1974), 118–122.Google Scholar

[338] F., Lust-Piquard, Inégalités de Khintchine daus Cp (1 < p < ∞), C.R. Acad. Sci. Paris 303 (1986), 289–292.Google Scholar

[339] F., Lust-Piquard and G., Pisier, Noncommutative Khintchine and Paley inequalities, Arkiv Mat. 29 (1991), 241–260.Google Scholar

[340] M., Manstavicius, p-variation of strong Markov processes, Ann. Probab. 32 (2004), 2053–2066.Google Scholar

[341] T., Martínez and J. L., Torrea, Operator-valued martingale transforms, Tohoku Math. J. 52 (2000), 449–474.Google Scholar

[342] J., Matoušek, On embedding trees into uniformly convex Banach spaces, Israel J. Math. 114 (1999), 221–237.Google Scholar

[343] B., Maurey, Systémes de Haar, in Séminaire Maurey–Schwartz, Ecole Polytechnique, Paris, 74–75.

[344] B., Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp, with an Astérisque, no. 11, Société Mathématique de France, Paris, 1974.Google Scholar

[345] B., Maurey, Type et cotype dans les espaces munis de structures locales inconditionnelles, in Séminaire Maurey-Schwartz 1973–1974: Espaces Lp, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. 24 and 25, Centre de Math., École Polytech., Paris, 1974.Google Scholar

[346] B., Maurey, Construction de suites symetriques, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), A679–A681.Google Scholar

[347] B., Maurey, Type, cotype and K-convexity, in Handbook of the geometry of Banach spaces, Vol. II, North-Holland, Amsterdam, 2003, 1299–1332.Google Scholar

[348] B., Maurey and G., Pisier, SÉries de variables alÉatoires vectorielles indépendantes et priétés géométriques des espaces de Banach, Studia Math. 58 (1976), 45–90.Google Scholar

[349] T., McConnell, On Fourier multiplier transformations of Banach-valued functions, Trans. Am. Math. Soc. 285 (1984), 739–757.Google Scholar

[350] T., Mei, BMO is the intersection of two translates of dyadic BMO, C. R. Math. Acad. Sci.Paris 336 (2003), 1003–1006.Google Scholar

[351] M., Mendel and A., Naor, Markov convexity and local rigidity of distorted metrics, J. Eur. Math. Soc. 15 (2013), 287–337.Google Scholar

[352] P. W., Millar, Path behavior of processes with stationary independent increments, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 17 (1971), 53–73.Google Scholar

[353] M., Milman, Fourier type and complex interpolation. Proc. Am. Math. Soc. 89 (1983), 246–248.Google Scholar

[354] M., Milman, Complex interpolation and geometry of Banach spaces, Ann. Mat. Pura Appl. 136 (1984), 317–328.Google Scholar

[355] I., Monroe, On the γ-variation of processes with stationary independent increments, Ann. Math. Statist. 43 (1972), 1213–1220.Google Scholar

[356] M., Musat, On the operator space UMD property and non-commutative martingale inequalities, PhD Thesis, University of Illinois at Urbana-Champaign, 2002.

[357] A., Naor, Y., Peres, O., Schramm and S., Sheffield, Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces, Duke Math. J. 134 (2006), 165–197.Google Scholar

[358] A., Naor and T., Tao, Random martingales and localization of maximal inequalities, J. Funct. Anal. 259 (2010), 731–779.Google Scholar

[359] F., Nazarov, G., Pisier, S., Treil and A., Volberg, Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts, J. Reine Angew. Math. 542 (2002), 147–171.Google Scholar

[360] F., Nazarov and S., Treil, Theweighted norm inequalities forHilbert transform are nowtrivial, C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 717–722.Google Scholar

[361] F., Nazarov and S., Treil, The hunt for a Bellman function: applications to estimates for singular integral operators and to other classical problems of harmonic analysis, St. Petersburg Math. J. 8 (1997), 721–824.Google Scholar

[362] F., Nazarov, S., Treil and A., Volberg, The Bellman functions and two-weight inequalities for Haar multipliers, J. Am. Math. Soc. 12 (1999), 909–928.Google Scholar

[363] F., Nazarov, S., Treil and A., Volberg, Counterexample to infinite dimensional Carleson embedding theorem, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), 383–388.Google Scholar

[364] E., Nelson, The free Markoff field, J. Funct. Anal. 12 (1973), 211–227.Google Scholar

[365] E., Nelson, Notes on non-commutative integration, J. Funct. Anal. 15 (1974), 103–116.Google Scholar

[366] J., Neveu, Sur l'espérance conditionnelle par rapport á un mouvement brownien, Ann. Inst. H. Poincaré Sect. B (N.S.) 12 (1976), 105–109.Google Scholar

[367] G., Nordlander, The modulus of convexity in normed linear spaces, Ark. Mat. 4 (1960), 15–17.Google Scholar

[368] M. I., Ostrovskii, On metric characterizations of some classes of Banach spaces, C. R. Acad. Bulgare Sci. 64 (2011), 775–784.Google Scholar

[369] M. I., Ostrovskii, Embeddability of locally finite metric spaces into Banach spaces is finitely determined, Proc. Am. Math. Soc. 140 (2012), 2721–2730.Google Scholar

[370] M. I., Ostrovskii, Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphs, Anal. Geom. Metr. Spaces 2 (2014), 154–168.Google Scholar

[371] M. I., Ostrovskii, Radon-Nikodym property and thick families of geodesics, J. Math. Anal. Appl. 409 (2014), 906–910.Google Scholar

[372] V. I., Ovchinnikov, The method of orbits in interpolation theory, Math. Rep. 1 (1984), 349–515.Google Scholar

[373] J., Parcet and N., Randrianantoanina, Gundy's decomposition for non-commutative martingales and applications, Proc. London Math. Soc. 93 (2006), 227–252.Google Scholar

[374] M., Pavlović, Uniform c -convexity of Lp, 0 < p 1, Publ. Inst. Math. (Beograd) (N.S.) 43 (1988), 117–124.Google Scholar

[375] M., Pavlović, On the complex uniform convexity of quasi-normed spaces, in Math. Balkanica (N.S.) 5 (1991), 92–98.Google Scholar

[376] J., Peetre, Sur la transformation de Fourier des fonctions á valeurs vectorielles, Rend. Sem. Mat. Univ. Padova 42 (1969), 15–26.Google Scholar

[377] M. C., Pereyra, Lecture notes on dyadic harmonic analysis: Second Summer School in Analysis and Mathematical Physics (Cuernavaca, 2000), Contemp. Math. 289, 1–60.

[378] S., Petermichl, Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), 455–460.Google Scholar

[379] S., Petermichl, S., Treil and A., Volberg, Why the Riesz transforms are averages of the dyadic shifts? in Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000), Publ. Mat., extra volume (2002), 209–228.Google Scholar

[380] B. J., Pettis, A proof that every uniformly convex space is reflexive, Duke Math. J. 5 (1939), 249–253.Google Scholar

[381] R. R., Phelps, Dentability and extreme points in Banach spaces, J. Funct. Anal. 17 (1974), 78–90.Google Scholar

[382] M., Piasecki, A geometrical characterization of AUMD Banach spaces via subharmonic functions, Demonstratio Math. 30 (1997), 641–654.Google Scholar

[383] M., Piasecki, A characterization of complex AUMD Banach spaces via tangent martingales, Demonstratio Math. 30 (1997), 715–728.Google Scholar

[384] J., Picard, A tree approach to p-variation and to integration, Ann. Probab. 36 (2008), 2235–2279.Google Scholar

[385] S., Pichorides, On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44 (1972), 165–179.Google Scholar

[386] G., Pisier, Un exemple concernant la super-réflexivité, Séminaire Maurey-Schwartz 1974- 1975, Annexe 2, http://www.numdam.org/.

[387] G., Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326–350.Google Scholar

[388] G., Pisier, Some applications of the complex interpolationmethod to Banach lattices, J. Anal. Math. Jerusalem 35 (1979), 264–281.Google Scholar

[389] G., Pisier, Holomorphic semigroups and the geometry of Banach spaces, Ann. Math. 115 (1982), 375–392.Google Scholar

[390] G., Pisier,On the duality between type and cotype, in Martingale theory in harmonic analysis and Banach spaces (Cleveland, Ohio, 1981), Lecture Notes in Mathematics 939, Springer, Berlin, 1982, 131–144.Google Scholar

[391] G., Pisier, Probabilistic methods in the geometry of Banach spaces, in Probability and analysis (Varenna, 1985), Lecture Notes in Mathematics 1206, Springer, Berlin, 1986, 167–241.Google Scholar

[392] G., Pisier, The dual J∗ of the James space has cotype 2 and the Gordon-Lewis property, Math. Proc. Cambridge Philos. Soc. 103 (1988), 323–331.Google Scholar

[393] G., Pisier, The Kt-functional for the interpolation couple L1(A0), L∞ (A1), J. Approx. Theory 73 (1993), 106–117.Google Scholar

[394] G., Pisier, Complex interpolation and regular operators between Banach lattices, Arch.Math. (Basel) 62 (1994), 261–269.Google Scholar

[395] G., Pisier, Noncommutative vector valued Lp-spaces and completely p-summing maps, Soc. Math. France Astérisque 237 (1998), 131 pp.Google Scholar

[396] G., Pisier, Remarks on the non-commutative Khintchine inequalities for 0 < p < 2, J. Funct. Anal. 256 (2009), 4128–4161.Google Scholar

[397] G., Pisier, Complex interpolation between Hilbert, Banach and operator spaces, Mem. Am. Math. Soc. 208 (2010), 78 pp.Google Scholar

[398] G., Pisier and É., Ricard, The non-commutative Khintchine inequalities for 0 < p < 1, J.Inst. Math. Jussieu, forthcoming.

[399] G., Pisier and Q., Xu, Random series in the real interpolation spaces between the spaces vp, in Geometrical aspects of functional analysis (1985/86), Lecture Notes in Mathematics 1267, Springer, Berlin, 1987, 185–209.Google Scholar

[400] G., Pisier and Q., Xu, The strong p-variation of martingales and orthogonal series, Probab. Theory Related Fields 77 (1988), 497–514.Google Scholar

[401] G., Pisier and Q., Xu, Non-commutative martingale inequalities, Comm. Math. Phys. 189 (1997), 667–698.Google Scholar

[402] G., Pisier and Q., Xu, Non-commutative Lp-spaces, in Handbook of the geometry of Banach spaces, Vol. II, North-Holland, Amsterdam, 2003, 1459–1517.Google Scholar

[403] D., Potapov, F., Sukochev and Q., Xu, On the vector-valued Littlewood-Paley-Rubio de Francia inequality, Rev. Mat. Iberoam. 28 (2012), 839–856.Google Scholar

[404] V., Pták, Biorthogonal systems and reflexivity of Banach spaces, Czechoslovak Math. J. 9 (1959), 319–326.Google Scholar

[405] Y., Qiu, On the UMD constants for a class of iterated Lp (Lq) spaces, J. Funct. Anal. 262 (2012), 2409–2429.Google Scholar

[406] Y., Qiu, On the OUMD property for the column Hilbert space C, Indiana Univ. Math. J. 61 (2012), 2143–2156.

[407] Y., Qiu, A remark on the complex interpolation for families of Banach spaces, Rev. Mat. Iber. 31 (2015), 439–460.Google Scholar

[408] Y., Qiu, A non-commutative version of Lépingle-Yor martingale inequality, Statist. Probab. Lett. 91 (2014), 52–54.Google Scholar

[409] M., Raja, Finite slicing in superreflexive Banach spaces, J. Funct. Anal. 268 (2015), 2672–2694.Google Scholar

[410] N., Randrianantoanina, Non-commutative martingale transforms, J. Funct. Anal. 194 (2002), 181–212.Google Scholar

[411] N., Randrianantoanina, Square function inequalities for non-commutative martingales, Israel J. Math. 140 (2004), 333–365.Google Scholar

[412] N., Randrianantoanina, A weak-type inequality for non-commutative martingales and applications, Proc. London Math. Soc. 91 (2005), 509–544.Google Scholar

[413] N., Randrianantoanina, Conditioned square functions for noncommutative martingales, Ann. Probab. 35 (2007), 1039–1070.Google Scholar

[414] N., Randrianantoanina, A remark on maximal functions for noncommutative martingales, Arch. Math. (Basel) 101 (2013), 541–548.Google Scholar

[415] H. P., Rosenthal, On the subspaces of Lp (p > 2) spanned by sequences of independent random variables, Israel J. Math. 8 (1970), 273–303.Google Scholar

[416] H. P., Rosenthal, Martingale proofs of a general integral representation theorem, in Analysis at Urbana, Vol. II, Cambridge University Press, Cambridge, 1989, 294–356.Google Scholar

[417] J. L. Rubio de, Francia, Fourier series and Hilbert transforms with values in UMD Banach spaces, Studia Math. 81 (1985), 95–105.Google Scholar

[418] J. L. Rubio de, Francia, Martingale and integral transforms of Banach space valued functions, in Probability and Banach spaces (Zaragoza, 1985), Lecture Notes in Mathematics 1221, Springer, Berlin, 1986, 195–222.Google Scholar

[419] W., Schachermayer, For a Banach space isomorphic to its square the Radon-Nikodym property and the Krein-Milman property are equivalent, Studia Math. 81 (1985), 329–339.Google Scholar

[420] W., Schachermayer, The sum of two Radon-Nikodym-sets need not be a Radon-Nikodým-set, Proc. Am. Math. Soc. 95 (1985), 51–57.

[421] W., Schachermayer, Some remarks concerning the Krein-Milman and the Radon-Nikodým property of Banach spaces, in Banach spaces (Columbia, Mo., 1984), Lecture Notes in Mathematics 1166, Springer, Berlin, 1985, 169–176.Google Scholar

[422] W., Schachermayer, The Radon-Nikodým property and the Krein-Milman property are equivalent for strongly regular sets, Trans. Am. Math. Soc. 303 (1987), 673–687.Google Scholar

[423] W., Schachermayer, A Sersouri and E. Werner, Moduli of nondentability and the Radon-Nikodým property in Banach spaces, Israel J. Math. 65 (1989), 225–257.Google Scholar

[424] J. J., Schäffer and K., Sundaresan, Reflexivity and the girth of spheres, Math. Ann. 184 (1969/1970), 163–168.Google Scholar

[425] J., Schwartz, A remark on inequalities of Calderón-Zygmund type for vector-valued functions, Comm. Pure Appl. Math. 14 (1961), 785–799.Google Scholar

[426] T., Simon, Small ball estimates in p-variation for stable processes, J. Theoret. Probab. 17 (2004), 979–1002.Google Scholar

[427] J., Stafney, The spectrum of an operator on an interpolation space, Trans. Am. Math. Soc. 144 (1969), 333–349.Google Scholar

[428] C., Stegall, The Radon-Nikodym property in conjugate Banach spaces, Trans. Am. Math. Soc. 206 (1975), 213–223.Google Scholar

[429] C., Stegall, The duality between Asplund spaces and spaces with the Radon-Nikodym property, Israel J. Math. 29 (1978), 408–412.Google Scholar

[430] S., Szarek, On the best constants in the Khinchin inequality, Studia Math. 58 (1976), 197–208.Google Scholar

[431] M., Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Inst. Hautes Études Sci. Publ. Math. 81 (1995), 73–205.Google Scholar

[432] N., Tomczak-Jaegermann, The moduli of smoothness and convexity and the Rademacher averages of trace classes Sp (1 ≤ p < ∞), Studia Math. 50 (1974), 163–182.Google Scholar

[433] D. A., Trautman, A note on MT operators, Proc. Am. Math. Soc. 97 (1986), 445–448.Google Scholar

[434] F., Watbled, Complex interpolation of a Banach space with its dual, Math. Scand. 87 (2000), 200–210.Google Scholar

[435] E., Werner,Nondentable solid subsets in Banach lattices failing RNP: applications to renormings, Proc. Am. Math. Soc. 107 (1989), 611–620.Google Scholar

[436] T., Wolff, A note on interpolation spaces, in Harmonic analysis (Minneapolis, Minn., 1981), Lecture Notes in Mathematics 908, Springer, Berlin, 1982, 199–204.Google Scholar

[437] W., Woyczyński, On Marcinkiewicz-Zygmund laws of large numbers in Banach spaces and related rates of convergence, Probab. Math. Statist. 1 (1980), 117–131.Google Scholar

[438] Q., Xu, Espaces d'interpolation réels entre les espaces Vp : propriétés géométriques et applications probabilistes, Publ. Math. Univ. Paris VII 28 (1988), 77–123.Google Scholar

[439] Q., Xu, Real interpolation of some Banach lattices valued Hardy spaces, Bull. Sci. Math. 116 (1992), 227–246.Google Scholar

[440] Q., Xu, H∞ functional calculus and maximal inequalities for semigroups of contractions on vector-valued Lp-spaces, preprint, Arxiv, 2014.