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Published online by Cambridge University Press:  19 July 2019

Andreas Defant
Affiliation:
Carl V. Ossietzky Universität Oldenburg, Germany
Domingo García
Affiliation:
Universitat de València, Spain
Manuel Maestre
Affiliation:
Universitat de València, Spain
Pablo Sevilla-Peris
Affiliation:
Universitat Politècnica de València, Spain
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References

Aizenberg, Lev. 2000. Multidimensional analogues of Bohr’s theorem on power series. Proc. Amer. Math. Soc., 128(4), 11471155. (Cited on pages 204 and 504).CrossRefGoogle Scholar
Albiac, Fernando, and Kalton, Nigel J. 2006. Topics in Banach space theory. Graduate Texts in Mathematics, vol. 233. New York: Springer. (Cited on page 350).Google Scholar
Albuquerque, Nacib, Bayart, Frédéric, Pellegrino, Daniel, and Seoane-Sepúlveda, Juan B. 2014. Sharp generalizations of the multilinear Bohnenblust–Hille inequality. J. Funct. Anal., 266(6), 37263740. (Cited on page 485).Google Scholar
Albuquerque, Nacib, Bayart, Frédéric, Pellegrino, Daniel, and Seoane-Sepúlveda, Juan B. 2016. Optimal Hardy–Littlewood type inequalities for polynomials and multilinear operators. Israel J. Math., 211(1), 197220. (Cited on pages 485 and 643).CrossRefGoogle Scholar
Aleman, Alexandru, Olsen, J. Fredrik, and Saksman, Eero. 2014. Fourier multipliers for Hardy spaces of Dirichlet series. Int. Math. Res. Not. IMRN, 4368–4378. (Cited on page 293).Google Scholar
Aleman, Alexandru, Olsen, J. Fredrik, and Saksman, Eero. 2015. Fatou and brother Riesz theorems in the infinite dimensional polydisc. J. Anal. Math. to appear 2019. (Cited on page 335).Google Scholar
Alencar, Raymundo. 1985. On reflexivity and basis for P(mE). Proc. Roy. Irish Acad. Sect. A, 85(2), 131138. (Cited on page 533).Google Scholar
Apostol, Tom M. 1976. Introduction to analytic number theory. Undergraduate Texts in Mathematics. New York: Springer. (Cited on page 35).Google Scholar
Apostol, Tom M. 1990. Modular functions and Dirichlet series in number theory. Second edn. Graduate Texts in Mathematics, vol. 41. New York: Springer. (Cited on pages 35, 90 and 91).Google Scholar
Aron, Richard M. and Globevnik, Josip. 1989. Analytic functions on c0. Rev. Mat. Univ. Complut. Madrid, 2(suppl.), 2733. Congress on Functional Analysis (Madrid, 1988). (Cited on pages 229 and 409).Google Scholar
Aron, Richard M., Hervés, Carlos, and Valdivia, Manuel. 1983. Weakly continuous mappings on Banach spaces. J. Funct. Anal., 52(2), 189204. (Cited on page 409).Google Scholar
Baernstein II, Albert, and Culverhouse, Robert C. 2002. Majorization of sequences, sharp vector Khinchin inequalities, and bisubharmonic functions. Studia Math., 152(3), 231248. (Cited on page 151).Google Scholar
Balasubramanian, Ramachandran, Calado, Bruno, and Queffélec, Hervé. 2006. The Bohr inequality for ordinary Dirichlet series. Studia Math., 175(3), 285304. (Cited on pages 35, 229 and 314).Google Scholar
Balazard, Michel. 1989. Remarques sur un théorème de G. Halász et A. Sárközy. Bull. Soc. Math. France, 117(4), 389413. (Cited on page 229).Google Scholar
Barroso, Jorge A., Matos, Mário C., and Nachbin, Leopoldo. 1977. On holomorphy versus linearity in classifying locally convex spaces. Pages 3174. North–Holland Math. Studies, Vol. 12, Notas de Mat., No. 54 of: Infinite dimensional holomorphy and applications (Proc. Internat. Sympos., Univ. Estadual de Campinas, São Paulo, 1975). Amsterdam: North-Holland. (Cited on page 409).Google Scholar
Bayart, Frédéric. 2002a. Hardy spaces of Dirichlet series and their composition operators. Monatsh. Math., 136(3), 203236. (Cited on pages 204, 288, 314 and 335).CrossRefGoogle Scholar
Bayart, Frédéric. 2002b. Opérateurs de composition sur des espaces de séries de Dirichlet et problèmes d’hypercyclicité simultanée. PhD thesis, Université des Sciences et Technologie Lille, Lille, France. (Cited on pages 288, 298 and 314).Google Scholar
Bayart, Frédéric. 2012. Maximum modulus of random polynomials. Q. J. Math., 63(1), 2139. (Cited on pages 471, 504 and 530).CrossRefGoogle Scholar
Bayart, Frédéric. 2018. Multiple summing maps: coordinatewise summability, inclusion theorems and p-Sidon sets. J. Funct. Anal., 274(4), 11291154. (Cited on page 644).Google Scholar
Bayart, Frédéric, Pellegrino, Daniel, and Seoane-Sepúlveda, Juan B. 2014. The Bohr radius of the n-dimensional polydisk is equivalent to . Adv. Math., 264, 726746. (Cited on pages 151, 152, 204 and 267).CrossRefGoogle Scholar
Bayart, Frédéric, Defant, Andreas, Frerick, Leonhard, Maestre, Manuel, and Sevilla-Peris, Pablo. 2017. Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables. Math. Ann., 368(1–2), 837– 876. (Cited on pages 267, 288, 314 and 335).CrossRefGoogle Scholar
Bayart, Frédéric, Defant, Andreas, and Schlüters, Sunke. 2019. Monomial convergence for holomorphic functions on r . J. Anal. Math., to appear. (Cited on pages 229, 504 and 530).Google Scholar
Beauzamy, Bernard and Lapresté, J.-T. 1984. Modèles étalés des espaces de Banach. Travaux en Cours. [Works in Progress]. Paris. Hermann. (Cited on page 553).Google Scholar
Benedek, Agnes and Panzone, Rafael. 1961. The space Lp, with mixed norm. Duke Math. J., 28, 301–324. (Cited on page 151).Google Scholar
Bennett, G. 1973. Inclusion mappings between lp spaces. J. Funct. Anal., 13, 2027. (Cited on page 345).Google Scholar
Blasco, Oscar. 1987. Positive p-summing operators on Lp-spaces. Proc. Amer. Math. Soc., 100(2), 275280. (Cited on page 611).Google Scholar
Blasco, Oscar. 1988. Boundary values of functions in vector-valued Hardy spaces and geometry on Banach spaces. J. Funct. Anal., 78(2), 346364. (Cited on page 611).CrossRefGoogle Scholar
Blasco, Oscar and Pavlović, Miroslav. 2003. Complex convexity and vector-valued Littlewood–Paley inequalities. Bull. London Math. Soc., 35(6), 749758. (Cited on page 643).Google Scholar
Blei, Ron C. 1979. Fractional Cartesian products of sets. Ann. Inst. Fourier (Grenoble), 29(2), 79105. (Cited on pages 150 and 151).Google Scholar
Blei, Ron C. and Fournier, John J. F. 1989. Mixed-norm conditions and Lorentz norms. Pages 57–78 of: Commutative harmonic analysis (Canton, NY, 1987). Contemp. Math., vol. 91. Providence, RI: Amer. Math. Soc. (Cited on page 151).Google Scholar
Blower, Gordon and Ransford, Thomas. 2004. Complex uniform convexity and Riesz measures. Canad. J. Math., 56(2), 225245. (Cited on page 629).CrossRefGoogle Scholar
Boas, Harold P. 1997. The football player and the infinite series. Notices Amer. Math. Soc., 44(11), 14301435. (Cited on pages 35 and 110).Google Scholar
Boas, Harold P. 2000. Majorant series. J. Korean Math. Soc., 37(2), 321337. Several complex variables (Seoul, 1998). (Cited on pages 204, 471 and 504).Google Scholar
Boas, Harold P. and Khavinson, Dmitry. 1997. Bohr’s power series theorem in several variables. Proc. Amer. Math. Soc., 125(10), 29752979. (Cited on pages 204 and 504).Google Scholar
Bogdanowicz, W. 1957. On the weak continuity of the polynomial functionals defined on the space c0. Bull. Acad. Polon. Sci. Cl. III., 5, 243246, XXI. (Cited on page 409).Google Scholar
Bohnenblust, Henri F. and Hille, Einar. 1931. On the absolute convergence of Dirichlet series. Ann. Math. (2), 32(3), 600622. (Cited on pages xi, xv, xv, xvi, 75, 110, 150, 151 and 267).CrossRefGoogle Scholar
Bohr, Harald. 1913. Darstellung der gleichmäßigen Konvergenzabszisse einer Dirichletschen Reihe als Funktion der Koeffizienten der Reihe. Arch. der Math. Phys. (3), 21, 326330. (Cited on page 35).Google Scholar
Bohr, Harald. 1913a. Über die Bedeutung der Potenzreihen unendlich vieler Variabeln in der Theorie der Dirichlet–schen Reihen . Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl., 441–488. (Cited on pages xi, xii, xv, 35, 90, 91, 110, 266, 267 and 530).Google Scholar
Bohr, Harald. 1913b. Über die gleichmäßige Konverenz Dirichletscher Reihen. J. Reine Angew. Math., 143, 203211. (Cited on page 35).CrossRefGoogle Scholar
Bohr, Harald. 1914. A theorem concerning power series. Proc. London Math. Soc. (2), 13, 15. (Cited on pages xii, xvi, xvii and 204).Google Scholar
Bohr, Harald. 1918. Zur Theorie der allgemeinen Dirichletschen Reihen. Math. Ann., 79, 136156. (Cited on page 90).Google Scholar
Bombieri, Enrico. 1962. Sopra un teorema di H. Bohr e G. Ricci sulle funzioni maggioranti delle serie di potenze. Boll. Un. Mat. Ital. (3), 17, 276282. (Cited on page 501).Google Scholar
Bombieri, Enrico and Bourgain, Jean. 2004. A remark on Bohr’s inequality. Int. Math. Res. Not., 4307–4330. (Cited on page 502).Google Scholar
Bombieri, Enrico and Bourgain, Jean. 2009. On Kahane’s ultraflat polynomials. J. Eur. Math. Soc. (JEMS), 11(3), 627703. (Cited on page 214).Google Scholar
Bonami, Aline. 1970. Étude des coefficients de Fourier des fonctions de Lp (G). Ann. Inst. Fourier (Grenoble), 20(fasc. 2), 335402. (Cited on page 204).Google Scholar
Bonet, José. 2018. The Fréchet Schwartz algebra of uniformly convergent Dirichlet series. Proc. Edinb. Math. Soc., 61(4), 933942. (Cited on page 36).Google Scholar
Brevig, Ole Fredrik. 2014. On the Sidon constant for Dirichlet polynomials. Bull. Sci. Math., 138(5), 656664. (Cited on page 229).Google Scholar
Bukhvalov, A. V. and Danilevich, A. A. 1982. Boundary properties of analytic and harmonic functions with values in a Banach space. Mat. Zametki, 31(2), 203– 214, 317. (Cited on page 583).Google Scholar
Cahen, Eugène. 1894. Sur la fonction ζ(s) de Riemann et sur des fonctions analogues. Ann. Sci. Éc. Norm. Supér. (3), 11, 75164. (Cited on page 35).CrossRefGoogle Scholar
Carando, Daniel, Defant, Andreas, and Sevilla-Peris, Pablo. 2014. Bohr’s absolute convergence problem for Hp-Dirichlet series in Banach spaces. Anal. PDE, 7(2), 513527. (Cited on pages 314, 643 and 663).Google Scholar
Carando, Daniel, Defant, Andreas, and Sevilla-Peris, Pablo. 2015a. The Bohnenblust– Hille inequality combined with an inequality of Helson. Proc. Amer. Math. Soc., 143(12), 52335238. (Cited on page 314).Google Scholar
Carando, Daniel, Defant, Andreas, García, Domingo, Maestre, Manuel, and Sevilla-Peris, Pablo. 2015b. The Dirichlet–Bohr radius. Acta Arith., 171(1), 2337. (Cited on page 229).Google Scholar
Carando, Daniel, Defant, Andreas, and Sevilla-Peris, Pablo. 2016. Some polynomial versions of cotype and applications. J. Funct. Anal., 270(1), 6887. (Cited on pages 623, 643 and 663).Google Scholar
Carando, Daniel, Defant, Andreas, and Sevilla-Peris, Pablo. 2018. Almost sure-sign convergence of Hardy-type Dirichlet series. J. Anal. Math., 135(1), 225247. (Cited on pages 180 and 663).Google Scholar
Carando, Daniel, Marceca, Felipe, and Sevilla-Peris, Pablo. 2019. Hausdorff–Young type inequalities for vector-valued Dirichlet series. arXiv:1904.00041. (Cited on page 643).Google Scholar
Carl, Bernd. 1974. Absolut-(p, 1)-summierende identische Operatoren von lu in lv. Math. Nachr., 63, 353360. (Cited on page 345).Google Scholar
Carlson, Fritz. 1922. Contributions à la théorie des séries de Dirichlet. Note I. Ark. Mat. Astron. Fys., 16(18), 119. (Cited on pages 35 and 288).Google Scholar
Casazza, Peter G. and Nielsen, N. J. 1997. A Gaussian average property of Banach spaces. Illinois J. Math., 41(4), 559576. (Cited on pages 628 and 643).Google Scholar
Cole, Brian J. and Gamelin, Theodor W. 1986. Representing measures and Hardy spaces for the infinite polydisk algebra. Proc. London Math. Soc. (3), 53(1), 112142. (Cited on pages xiv, 128, 288, 334 and 335).CrossRefGoogle Scholar
Davie, A. M. 1973. Quotient algebras of uniform algebras. J. London Math. Soc. (2), 7, 3140. (Cited on page 151).Google Scholar
Davis, William J., Garling, David J. H., and Tomczak-Jaegermann, Nicole. 1984. The complex convexity of quasinormed linear spaces. J. Funct. Anal., 55(1), 110150. (Cited on pages 628 and 643).Google Scholar
de la Bretèche, Régis. 2008. Sur l’ordre de grandeur des polynômes de Dirichlet. Acta Arith., 134(2), 141148. (Cited on page 229).Google Scholar
Defant, Andreas and Floret, Klaus. 1993. Tensor norms and operator ideals. North-Holland Mathematics Studies, vol. 176. Amsterdam: North-Holland. (Cited on pages xxiv, xxiv, 150, 350, 434, 623 and 624).Google Scholar
Defant, Andreas and Frerick, Leonhard. 2006. A logarithmic lower bound for multidimensional Bohr radii. Israel J. Math., 152, 1728. (Cited on pages 204 and 504).Google Scholar
Defant, Andreas and Frerick, Leonhard. 2011. The Bohr radius of the unit ball of np. J. Reine Angew. Math., 660, 131147. (Cited on pages 204, 504, 553 and 564).Google Scholar
Defant, Andreas and Kalton, Nigel. 2005. Unconditionality in spaces of m-homogeneous polynomials. Q. J. Math., 56(1), 5364. (Cited on page 553).Google Scholar
Defant, Andreas and Mastyło, Mieczysław. 2016a. Bohnenblust–Hille inequalities for Lorentz spaces via interpolation. Anal. PDE, 9(5), 12351258. (Cited on page 151).Google Scholar
Defant, Andreas and Mastyło, Mieczysław. 2016b. Lp-norms and Mahler’s measure of polynomials on the n-dimensional torus. Constr. Approx., 44(1), 87101. (Cited on pages 204 and 554).Google Scholar
Defant, Andreas and Mastyło, Mieczysław. 2017. Norm estimates for random polynomials on the scale of Orlicz spaces. Banach J. Math. Anal., 11(2), 335347. (Cited on page 471).Google Scholar
Defant, Andreas and Pérez, Antonio. 2017. Optimal comparison of the p-norms of Dirichlet polynomials. Israel J. Math., 221(2), 837852. (Cited on pages 307 and 314).Google Scholar
Defant, Andreas and Pérez, Antonio. 2018. Hardy spaces of vector-valued Dirichlet series. Studia Math., 243(1), 5378. (Cited on pages 288, 335 and 611).Google Scholar
Defant, Andreas and Prengel, Christopher. 2009. Volume estimates in spaces of homogeneous polynomials. Math. Z., 261(4), 909932. (Cited on page 564).Google Scholar
Defant, Andreas and Sevilla-Peris, Pablo. 2009. A new multilinear insight on Littlewood’s 4/3-inequality. J. Funct. Anal., 256(5), 16421664. (Cited on page 643).Google Scholar
Defant, Andreas and Sevilla-Peris, Pablo. 2011. Convergence of Dirichlet polynomials in Banach spaces. Trans. Amer. Math. Soc., 363(2), 681697. (Cited on pages 472 and 663).Google Scholar
Defant, Andreas and Sevilla-Peris, Pablo. 2014. The Bohnenblust–Hille cycle of ideas from a modern point of view. Funct. Approx. Comment. Math., 50(1, [2013 on table of contents]), 55–127. (Cited on pages 110 and 150).Google Scholar
Defant, Andreas and Sevilla-Peris, Pablo. 2016. Unconditionality for m-homogeneous polynomials on . Studia Math., 232(1), 4555. (Cited on pages 204, 267 and 564).Google Scholar
Defant, Andreas, Díaz, Juan Carlos, García, Domingo, and Maestre, Manuel. 2001. Unconditional basis and Gordon–Lewis constants for spaces of polynomials. J. Funct. Anal., 181(1), 119145. (Cited on page 553).CrossRefGoogle Scholar
Defant, Andreas, Maestre, Manuel, and Sevilla-Peris, Pablo. 2002. Cotype 2 estimates for spaces of polynomials on sequence spaces. Israel J. Math., 129, 291315. (Cited on page 564).Google Scholar
Defant, Andreas, García, Domingo, and Maestre, Manuel. 2003. Bohr’s power series theorem and local Banach space theory. J. Reine Angew. Math., 557, 173197. (Cited on pages 204, 471, 472, 504 and 530).Google Scholar
Defant, Andreas, García, Domingo, and Maestre, Manuel. 2004. Estimates for the first and second Bohr radii of Reinhardt domains. J. Approx. Theory, 128(1), 5368. (Cited on page 204).Google Scholar
Defant, Andreas, García, Domingo, Maestre, Manuel, and Pérez-García, David. 2007. Extension of multilinear forms and polynomials from subspaces of L1-spaces. Houston J. Math., 33(3), 839860. (Cited on page 530).Google Scholar
Defant, Andreas, Maestre, Manuel, and Prengel, Christopher. 2008a. The arithmetic Bohr radius. Q. J. Math., 59(2), 189205. (Cited on pages 204, 504 and 530).Google Scholar
Defant, Andreas, García, Domingo, Maestre, Manuel, and Pérez-García, David. 2008b. Bohr’s strip for vector valued Dirichlet series. Math. Ann., 342(3), 533555. (Cited on page 663).Google Scholar
Defant, Andreas, Maestre, Manuel, and Prengel, Christopher. 2009. Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables. J. Reine Angew. Math., 634, 1349. (Cited on pages 267, 409 and 530).Google Scholar
Defant, Andreas, Popa, Dumitru, and Schwarting, Ursula. 2010. Coordinatewise multiple summing operators in Banach spaces. J. Funct. Anal., 259(1), 220242. (Cited on pages 151, 644 and 663).Google Scholar
Defant, Andreas, Frerick, Leonhard, Ortega-Cerdà, Joaquim, Ounaïes, Myriam, and Seip, Kristian. 2011. The Bohnenblust–Hille inequality for homogeneous polynomials is hypercontractive. Ann. of Math., 174(1), 485497. (Cited on pages 152, 204, 229 and 504).Google Scholar
Defant, Andreas, Maestre, Manuel, and Schwarting, Ursula. 2012. Bohr radii of vector valued holomorphic functions. Adv. Math., 231(5), 28372857. (Cited on page 643).Google Scholar
Defant, Andreas, Schwarting, Ursula, and Sevilla-Peris, Pablo. 2014. Estimates for vector valued Dirichlet polynomials. Monatsh. Math., 175(1), 89116. (Cited on pages 229 and 663).Google Scholar
Defant, Andreas, Mastyło, Mieczysław, and Pérez, Antonio. 2018a. Bohr’s phenomenon for functions on the Boolean cube. J. Funct. Anal., 275(11), 31153147. (Cited on page 204).Google Scholar
Defant, Andreas, Mastyło, Mieczysław, and Schlüters, Sunke. 2018b. On Bohr radii of finite dimensional complex Banach spaces. Funct. Approx. Comment. Math., 59(2), 251269. (Cited on page 564).Google Scholar
Diestel, J. and Uhl, J. J. Jr., 1977. Vector measures. With a foreword by B. J. Pettis Mathematical Surveys, No. 15. Providence, RI: American Mathematical Society. (Cited on pages xxiv, 434 and 601).Google Scholar
Diestel, Joe, Jarchow, Hans, and Tonge, Andrew. 1995. Absolutely summing operators. Cambridge Studies in Advanced Mathematics, vol. 43 Cambridge: Cambridge University Press. (Cited on pages 150, 180, 348, 349, 350 and 471).Google Scholar
Diestel, Joe, Fourie, Jan H., and Swart, Johan. 2008. The metric theory of tensor products. Providence, RI: American Mathematical Society. Grothendieck’s résumé revisited. (Cited on page 434).Google Scholar
Dilworth, Stephen J., Kalton, Nigel J., and Kutzarova, Denka. 2003. On the existence of almost greedy bases in Banach spaces. Studia Math., 159(1), 67101. Dedicated to Professor Aleksander Pełczyński on the occasion of his 70th birthday. (Cited on page 553).Google Scholar
Dimant, Verónica, and Sevilla-Peris, Pablo. 2016. Summation of coefficients of polynomials on p spaces. Publ. Mat., 60(2), 289310. (Cited on pages 484, 485 and 643).Google Scholar
Dineen, Seán. 1999. Complex analysis on infinite-dimensional spaces. Springer Monographs in Mathematics. London: Springer. (Cited on pages xiii, xiii, 407, 408, 409, 434, 531, 533 and 553).Google Scholar
Dineen, Seán and Timoney, Richard M. 1989. Absolute bases, tensor products and a theorem of Bohr. Studia Math., 94(3), 227234. (Cited on pages 204 and 504).Google Scholar
Dineen, Seán and Timoney, Richard M. 1991. On a problem of H. Bohr. Bull. Soc. Roy. Sci. Liège, 60(6), 401404. (Cited on page 204).Google Scholar
Dowling, Patrick N. 1987. The analytic Radon–Nikodým property in Lebesgue Bochner function spaces. Proc. Amer. Math. Soc., 99(1), 119122. (Cited on page 583).Google Scholar
Dunford, Nelson. 1938. Uniformity in linear spaces. Trans. Amer. Math. Soc., 44(2), 305356. (Cited on page 409).Google Scholar
Duoandikoetxea, Javier. 2001. Fourier analysis. Graduate Studies in Mathematics, vol. 29. Providence, RI: American Mathematical Society. Translated and revised from the 1995 Spanish original by David Cruz-Uribe. (Cited on page 574).Google Scholar
Duren, Peter L. 1970. Theory of Hp spaces. Pure and Applied Mathematics, Vol. 38. New York: Academic Press. (Cited on page 583).Google Scholar
Fatou, Pierre. 1906. Séries trigonométriques et séries de Taylor. Acta Math., 30(1), 335400. (Cited on page 583).Google Scholar
Fernique, Xavier. 1974. Des résultats nouveaux sur les processus gaussiens. C. R. Acad. Sci. Paris Sér. A, 278, 363365. (Cited on page 472).Google Scholar
Fetter, Helga and Gamboa de Buen, Berta. 1997. The James forest. London Mathematical Society Lecture Note Series, vol. 236. Cambridge: Cambridge University Press. With a foreword by Robert C. James and a prologue by Bernard Beauzamy. (Cited on page 553).Google Scholar
Floret, Klaus. 1997. Natural norms on symmetric tensor products of normed spaces. Note Mat., 17, 153188 (1999). (Cited on page 434).Google Scholar
Fournier, John J. F. 1987. Mixed norms and rearrangements: Sobolev’s inequality and Littlewood’s inequality. Ann. Mat. Pura Appl. (4), 148, 5176. (Cited on page 151).Google Scholar
Galicer, Daniel, Muro, Santiago, and Sevilla-Peris, Pablo. 2018a. Asymptotic estimates on the von Neumann inequality for homogeneous polynomials. J. Reine Angew. Math., 743, 213227. (Cited on page 472).Google Scholar
Galicer, Daniel, Mansilla, Martín, Muro, Santiago, and Sevilla-Peris, Pablo. 2019. Monomial convergence on r . Preprint. (Cited on pages 515 and 530).Google Scholar
Galicer, Daniel, Mansilla, Martín, and Muro, Santiago. 2019. Mixed Bohr radius in several variables. Trans. Amer. Math. Soc. to appear. (Cited on page 504).Google Scholar
García, Domingo, Maestre, Manuel, and Zalduendo, Ignacio. 2012. Algebras of functions with prescribed radii of boundedness and the spectra of H(U). Ann. Acad. Sci. Fenn. Math., 37(2), 445460. (Cited on page 409).Google Scholar
García-Cuerva, José and Parcet, Javier. 2004. Vector-valued Hausdorff–Young inequality on compact groups. Proc. London Math. Soc. (3), 88(3), 796816. (Cited on page 628).Google Scholar
García-Cuerva, José and Rubio de Francia, José L. 1985. Weighted norm inequalities and related topics. North-Holland Mathematics Studies, vol. 116. Amsterdam: North-Holland. (Cited on page 583).Google Scholar
García-Cuerva, José, Marco, José Manuel, and Parcet, Javier. 2003. Sharp Fourier type and cotype with respect to compact semisimple Lie groups. Trans. Amer. Math. Soc., 355(9), 35913609. (Cited on page 628).Google Scholar
Garnett, John B. 2007. Bounded analytic functions. First edn. Graduate Texts in Mathematics, vol. 236. New York: Springer. (Cited on pages 574 and 583).Google Scholar
Gâteaux, René. 1919. Fonctions d’une infinité de variables indépendantes. Bull. Soc. Math. France, 47, 7096. (Cited on page 408).Google Scholar
Gelbaum, Bernard R. and Gil de Lamadrid, Jesús. 1961. Bases of tensor products of Banach spaces. Pacific J. Math., 11, 12811286. (Cited on page 553).Google Scholar
Globevnik, Josip. 1975. On complex strict and uniform convexity. Proc. Amer. Math. Soc., 47, 175178. (Cited on page 643).CrossRefGoogle Scholar
Gordon, Y. and Lewis, D. R. 1974. Absolutely summing operators and local unconditional structures. Acta Math., 133, 2748. (Cited on page 553).Google Scholar
Gordon, Yehoram. 1985. Some inequalities for Gaussian processes and applications. Israel J. Math., 50(4), 265289. (Cited on page 472).Google Scholar
Grecu, Bogdan C. and Ryan, Raymond A. 2005. Schauder bases for symmetric tensor products. Publ. Res. Inst. Math. Sci., 41(2), 459469. (Cited on pages 532 and 553).Google Scholar
Haagerup, Uffe. 1981. The best constants in the Khintchine inequality. Studia Math., 70(3), 231283. (Cited on page 150).Google Scholar
Haagerup, Uffe and Pisier, Gilles. 1989. Factorization of analytic functions with values in noncommutative L1-spaces and applications. Can. J. Math., 41(5), 882906. (Cited on page 628).Google Scholar
Hardy, Godfrey H. and Littlewood, John E. 1930. A maximal theorem with function-theoretic applications. Acta Math., 54(1), 81116. (Cited on pages 530 and 583).Google Scholar
Hardy, Godfrey H. and Littlewood, John E. 1934. Bilinear forms bounded in space [p, q]. Q. J. Math., 5, 241–54. (Cited on pages 150 and 484).Google Scholar
Hardy, Godfrey H. and Riesz, Marcel. 1915. The general theory of Dirichlet’s series. Cambridge: Cambridge University Press. (Cited on pages 34 and 35).Google Scholar
Hardy, Godfrey H. and Wright, Edward M. 2008. An introduction to the theory of numbers. Sixth edn. Oxford: Oxford University Press. Revised by D. R. Heath-Brown and J. H. Silverman. (Cited on page 91).Google Scholar
Harris, Lawrence A. 1975. Bounds on the derivatives of holomorphic functions of vectors. Pages 145163. Actualités Aci. Indust., No. 1367 of: Analyse fonctionnelle et applications (Comptes Rendus Colloq. Analyse, Inst. Mat., Univ. Federal Rio de Janeiro, Rio de Janeiro, 1972). Paris: Hermann. (Cited on page 75).Google Scholar
Hartman, Philip. 1939. On Dirichlet series involving random coefficients. Amer. J. Math., 61, 955964. (Cited on page 180).Google Scholar
Hartogs, Fritz. 1906. Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen, insbesondere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten. Math. Ann., 62(1), 1– 88. (Cited on page 409).Google Scholar
Hedenmalm, Håkan. 2004. Dirichlet series and functional analysis. Pages 673–684 of: The legacy of Niels Henrik Abel. Berlin: Springer. (Cited on page 36).Google Scholar
Hedenmalm, Håkan and Eero, Saksman. 2003. Carleson’s convergence theorem for Dirichlet series. Pacific J. Math., 208(1), 85109. (Cited on page 298).Google Scholar
Hedenmalm, Håkan, Lindqvist, Peter, and Seip, Kristian. 1997. A Hilbert space of Dirichlet series and systems of dilated functions in L2 (0, 1). Duke Math. J., 86(1), 137. (Cited on pages xiv, 35, 92, 288 and 314).Google Scholar
Helson, Henry. 2005. Dirichlet series. Berkeley, CA: Henry Helson. (Cited on pages 35, 180 and 314).Google Scholar
Helson, Henry. 2006. Hankel forms and sums of random variables. Studia Math., 176(1), 8592. (Cited on page 314).Google Scholar
Helson, Henry and Lowdenslager, David. 1958. Prediction theory and Fourier series in several variables. Acta Math., 99, 165202. (Cited on page 335).Google Scholar
Hibert, David. 1935. Gesammelte Abhandlungen (Band 3). Berlin: Springer. (Cited on page xii).Google Scholar
Hilbert, David. 1909. Wesen und Ziele einer Analysis der unendlichvielen unabhängigen Variablen. Rend. del Circolo mat. di Palermo, 27, 5974. (Cited on pages xii and 55).Google Scholar
Hildebrand, Adolf and Tenenbaum, Gérald. 1993. Integers without large prime factors. J. Théor. Nombres Bordeaux, 5(2), 411484. (Cited on page 221).Google Scholar
Hille, Einar and Phillips, Ralph S. 1957. Functional analysis and semi-groups. American Mathematical Society Colloquium Publications, vol. 31. Revedn. Providence, RI: American Mathematical Society. (Cited on page 409).Google Scholar
Hoffman, Kenneth. 1962. Banach spaces of analytic functions. Prentice-Hall Series in Modern Analysis. Englewood Cliffs, NJ: Prentice-Hall. (Cited on page 335).Google Scholar
Höllig, Klaus. 1980. Diameters of classes of smooth functions. Pages 163175 of: Quantitative approximation (Proc. Internat. Sympos., Bonn, 1979). New York: Academic Press. (Cited on page 471).Google Scholar
Jarnicki, Marek and Pflug, Peter. 2011. Separately analytic functions. EMS Tracts in Mathematics, vol. 16. Zürich: European Mathematical Society (EMS). (Cited on page 409).Google Scholar
Jensen, Johan. L. W. V. 1884. Om Räkkers Konvergens. Zeuthen T. (5), 2, 6372. (Cited on pages 34 and 35).Google Scholar
Jensen, Johan. L. W. V. 1888. Sur une généralisation d’un théorème de Cauchy. C. R. Acad. Sci., Paris, 106, 833836. (Cited on pages 34 and 35).Google Scholar
Kahane, Jean-Pierre. 1960. Propriétés locales des fonctions à séries de Fourier aléatoires. Studia Math., 19, 125. (Cited on page 180).Google Scholar
Kahane, Jean-Pierre. 1964. Sur les sommes vectorielles ∑ ±un. C. R. Acad. Sci. Paris, 259, 25772580. (Cited on page 180).Google Scholar
Kahane, Jean-Pierre. 1980. Sur les polynômes à coefficients unimodulaires. Bull. London Math. Soc., 12(5), 321342. (Cited on page 216).Google Scholar
Kahane, Jean-Pierre. 1985. Some random series of functions. Second edn. Cambridge Studies in Advanced Mathematics, vol. 5. Cambridge: Cambridge University Press. (Cited on page 180).Google Scholar
Kaijser, Sten. 1978. Some results in the metric theory of tensor products. Studia Math., 63(2), 157170. (Cited on page 151).Google Scholar
König, Hermann. 1986. Eigenvalue distribution of compact operators. Operator Theory: Advances and Applications, vol. 16. Basel: Birkhäuser. (Cited on pages 345 and 350).Google Scholar
König, Hermann. 2014. On the best constants in the Khintchine inequality for Steinhaus variables. Israel J. Math., 203(1), 2357. (Cited on page 151).Google Scholar
König, Hermann and Kwapień, Stanisław. 2001. Best Khintchine type inequalities for sums of independent, rotationally invariant random vectors. Positivity, 5(2), 115152. (Cited on page 151).Google Scholar
Konyagin, Sergei V. and Queffélec, Hervé. 2001/02. The translation in the theory of Dirichlet series. Real Anal. Exchange, 27(1), 155175. (Cited on pages 229 and 298).Google Scholar
Krantz, Steven G. 2000. Fatou theorems old and new: an overview of the boundary behavior of holomorphic functions. J. Korean Math. Soc., 37(2), 139175. (Cited on page 583).Google Scholar
Kronecker, Leopold. 1884. Näherungsweise ganzzahlige Auflösung linearer Gleichungen. Monatsber. Königlich. Preuss. Akad. Wiss. Berlin, 1179–1193, 1271–1299. (Cited on page 91).Google Scholar
Kronecker, Leopold. 1968. Leopold Kronecker’s Werke. Bände I–V. Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften von K. Hensel. New York: Chelsea. (Cited on page 91).Google Scholar
Landau, Edmund. 1909a. Handbuch der Lehre von der Verteilung der Primzahlen. Erster Band. Leipzig: B. G. Teubner. (Cited on page 35).Google Scholar
Landau, Edmund. 1909b. Handbuch der Lehre von der Verteilung der Primzahlen. Zweiter Band. Leipzig: B. G. Teubner. (Cited on page 35).Google Scholar
Landau, Edmund. 1916, second edn. 1929, third edn. 1986, edited and suplemented by Dieter Gaier. Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie. Berlin: Springer. (Cited on page 204).Google Scholar
Ledoux, Michel and Talagrand, Michel. 2011. Probability in Banach spaces. Classics in Mathematics. Berlin: Springer. Isoperimetry and processes, Reprint of the 1991 edition. (Cited on pages 436, 445, 462 and 471).Google Scholar
Leja, Franciszek. 1950. Une nouvelle démonstration d’un théorème sur les séries de fonctions analytiques. Actas Acad. Ci. Lima, 13, 37. (Cited on page 409).Google Scholar
Lempert, László. 1999. The Dolbeault complex in infinite dimensions. II. J. Amer. Math. Soc., 12(3), 775793. (Cited on pages 517 and 530).Google Scholar
Lempert, László. 2000. Approximation of holomorphic functions of infinitely many variables. II. Ann. Inst. Fourier (Grenoble), 50(2), 423442. (Cited on page 526).Google Scholar
Li, Daniel and Queffélec, Hervé. 2004. Introduction à l’étude des espaces de Banach. Cours Spécialisés [Specialized Courses], vol. 12. Paris: Société Mathématique de France. Analyse et probabilités. [Analysis and probability theory]. (Cited on page 472).Google Scholar
Lindenstrauss, Joram and Tzafriri, Lior. 1977. Classical Banach spaces. I. Berlin: Springer. Sequence spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92. (Cited on pages 150 and 350).Google Scholar
Lindenstrauss, Joram and Tzafriri, Lior. 1979. Classical Banach spaces. II. Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97. Berlin: Springer. Function spaces. (Cited on page 350).Google Scholar
Littlewood, John E. 1930. On bounded bilinear forms in an infinite number of variables. Q. J. (Oxford Series), 1, 164174. (Citedon page150).Google Scholar
Littlewood, John E. 1966. On polynomials ∑n ±zm, ∑n eαmizm, z = eθi. J. London Math. Soc., 41, 367376. (Cited on page 216).Google Scholar
Lorentz, George G. 1966. Approximation of functions. New York: Holt. (Cited on page 180).Google Scholar
Mandelbrojt, Szolem. 1944. Dirichlet series. Rice Inst. Pamphlet, 31, 159272. (Cited on page 35).Google Scholar
Marcus, Michael B. and Rosen, Jay. 2006. Markov processes, Gaussian processes, and local times. Cambridge Studies in Advanced Mathematics, vol. 100. Cambridge: Cambridge University Press. (Cited on page 462).Google Scholar
Mastyło, Mieczysław and Szwedek, Radosław. 2017. Kahane–Salem–Zygmund polynomial inequalities via Rademacher processes. J. Funct. Anal., 272(11), 4483– 4512. (Cited on page 472).Google Scholar
Mateljević, Miodrag. 1979. The isoperimetric inequality in the Hardy class H1. Mat. Vesnik, 3 (16)(31)(2), 169178. (Cited on page 314).Google Scholar
Mateljević, Miodrag. 1980. The isoperimetric inequality and some extremal problems in H1. Pages 364369 of: Analytic functions, Kozubnik 1979 (Proc. Seventh Conf., Kozubnik, 1979). Lecture Notes in Math., vol. 798. Berlin: Springer. (Cited on page 314).Google Scholar
Maurey, Bernard and Pisier, Gilles. 1976. Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Studia Math., 58(1), 4590. (Cited on page 349).Google Scholar
Maurizi, Brian and Queffélec, Hervé. 2010. Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl., 16(5), 676692. (Cited on pages 35 and 229).CrossRefGoogle Scholar
Mazur, Stanisław and Orlicz, Władysław. 1934a. Grundlegende Eigenschaften der polynomischen Operationen I. Studia Math., 5, 5068. (Cited on page 75).Google Scholar
Mazur, Stanisław and Orlicz, Władysław. 1934b. Grundlegende Eigenschaften der polynomischen Operationen II. Studia Math.,, 5, 179189. (Cited on page 75).Google Scholar
Milman, Vitali D. and Schechtman, Gideon. 1986. Asymptotic theory of finite-dimensional normed spaces. Lecture Notes in Mathematics, vol. 1200. Berlin: Springer. With an appendix by M. Gromov. (Cited on page 471).Google Scholar
Muhanna, Y. Abu, Ali, R. M., and Ponnusamy, S. 2017. On the Bohr inequality. Pages 269–300 of: Govil, N. K., Mohapatra, R. N., Qazi, M., and Schmeisser, G. (eds), Progress in approximation theory and applicable complex analysis. New York: Springer. (Cited on page 204).Google Scholar
Mujica, Jorge. 1986. Complex analysis in Banach spaces. North-Holland Mathematics Studies, vol. 120. Amsterdam: North-Holland. Holomorphic functions and domains of holomorphy in finite and infinite dimensions, Notas de Matemática [Mathematical Notes], 107. (Reprinted by Dover Books on Mathematics, 2010). (Cited on page 408).Google Scholar
Odell, Edward. 1980. Applications of Ramsey theorems to Banach space theory. Pages 379404 of: Notes in Banach spaces. Austin: University of Texas Press. (Cited on page 553).Google Scholar
Paulsen, Vern and Singh, Dinesh. A simple proof of Bohr’s inequality. preprint. (Cited on page 204).Google Scholar
Pavlović, Miroslav. 1991. On the complex uniform convexity of quasi-normed spaces. Math. Balkanica (N.S.), 5(2), 9298. (Cited on page 643).Google Scholar
Pełczyński, Aleksander. 1957. A property of multilinear operations. Studia Math., 16, 173182. (Cited on page 533).Google Scholar
Pérez-García, David. 2004. The inclusion theorem for multiple summing operators. Studia Math., 165(3), 275290. (Cited on page 643).Google Scholar
Perron, Oskar. 1908. Zur Theorie der Dirichletschen Reihen. J. Reine Angew. Math., 134, 95143. (Cited on page 35).Google Scholar
Pietsch, Albrecht. 1980. Operator ideals. North-Holland Mathematical Library, vol. 20. Amsterdam: North-Holland. Translated from German by the author. (Cited on pages 345, 350, 471 and 556).Google Scholar
Pietsch, Albrecht. 1987. Eigenvalues and s-numbers. Cambridge Studies in Advanced Mathematics, vol. 13. Cambridge: Cambridge University Press. (Cited on pages 345 and 350).Google Scholar
Pisier, Gilles. 1978. Some results on Banach spaces without local unconditional structure. Compositio Math., 37(1), 319. (Cited on pages 553 and 628).Google Scholar
Pisier, Gilles. 1983. Some applications of the metric entropy condition to harmonic analysis. Pages 123154 of: Banach spaces, harmonic analysis, and probability theory (Storrs, Conn., 1980/1981). Lecture Notes in Math., vol. 995. Berlin: Springer. (Cited on page 471).Google Scholar
Pisier, Gilles. 1986. Factorization of linear operators and geometry of Banach spaces. CBMS Regional Conference Series in Mathematics, vol. 60. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI. (Cited on page 350).Google Scholar
Pisier, Gilles. 2016. Martingales in Banach spaces. Cambridge Studies in Advanced Mathematics, vol. 155. Cambridge: Cambridge University Press. (Cited on pages 583 and 629).Google Scholar
Prachar, Karl. 1957. Primzahlverteilung. Berlin: Springer. (Cited on page 226).Google Scholar
Praciano-Pereira, Tarsicio. 1981. On bounded multilinear forms on a class of lp spaces. J. Math. Anal. Appl., 81(2), 561568. (Cited on pages 484 and 485).Google Scholar
Prengel, Christopher. 2005. Domains of convergence in infinite dimensional holomorphy. PhD thesis, Universität Oldenburg, Oldenburg, Germany. (Cited on page 553).Google Scholar
Queffélec, Hervé. 1995. H. Bohr’s vision of ordinary Dirichlet series; old and new results. J. Anal., 3, 4360. (Cited on pages 151, 152, 180 and 229).Google Scholar
Queffélec, Hervé and Queffélec, Martine. 2013. Diophantine approximation and Dirichlet series. Harish-Chandra Research Institute Lecture Notes, vol. 2. New Delhi: Hindustan Book Agency. (Cited on pages 35 and 314).Google Scholar
Queffélec, Hervé and Saffari, Bahman. 1996. On Bernstein’s inequality and Kahane’s ultraflat polynomials. J. Fourier Anal. Appl., 2(6), 519582. (Cited on page 216).Google Scholar
Rudin, Walter. 1959. Some theorems on Fourier coefficients. Proc. Amer. Math. Soc., 10, 855859. (Cited on page 229).Google Scholar
Rudin, Walter. 1969. Function theory in polydiscs. New York: W. A. Benjamin. (Cited on pages 128, 331 and 335).Google Scholar
Rudin, Walter. 1980. Function theory in the unit ball of Cn. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241. New York: Springer. (Cited on page 128).Google Scholar
Rudin, Walter. 1987. Real and complex analysis. Third edn. New York: McGraw-Hill. (Cited on pages 568, 571, 572 and 583).Google Scholar
Rudin, Walter. 1990. Fourier analysis on groups. Wiley Classics Library. New York: John Wiley. Reprint of the 1962 original. (Cited on page 293).Google Scholar
Ryan, Raymond A. 1980. Applications of topological tensor products to infinite dimensional holomorphy. PhD thesis, Trinity College, Dublin, Ireland. (Cited on pages 434, 532 and 553).Google Scholar
Ryan, Raymond A. 1987. Holomorphic mappings on l1. Trans. Amer. Math. Soc., 302(2), 797811. (Cited on pages 517 and 530).Google Scholar
Ryan, Raymond A. 2002. Introduction to tensor products of Banach spaces. Springer Monographs in Mathematics. London: Springer. (Cited on page 434).Google Scholar
Salem, Raphaël, and Zygmund, Antoni. 1954. Some properties of trigonometric series whose terms have random signs. Acta Math., 91, 245301. (Cited on page 180).Google Scholar
Sawa, Jerzy. 1985. The best constant in the Khintchine inequality for complex Steinhaus variables, the case p = 1. Studia Math., 81(1), 107126. (Cited on page 150).Google Scholar
Schaefer, Helmut H. 1974. Banach lattices and positive operators. New York: Springer. Die Grundlehren der mathematischen Wissenschaften, Band 215. (Cited on page 611).Google Scholar
Schlumprecht, Thomas. March 2015. Infinite combinatorics and applications to Banach space theory (Course Notes, Math 663–301). (Cited on page 553).Google Scholar
Schütt, Carsten. 1978. Unconditionality in tensor products. Israel J. Math., 31(3-4), 209216. (Cited on page 553).Google Scholar
Schütt, Carsten. 1984. Entropy numbers of diagonal operators between symmetric Banach spaces. J. Approx. Theory, 40(2), 121128. (Cited on page 471).Google Scholar
Schwarting, Ursula. 2013. Vector valued Bohnenblust–Hille inequalities. PhD thesis, Universität Oldenburg, Oldenburg, Germany. (Cited on pages 643 and 663).Google Scholar
Shapiro, Harold S. 1951. Extremal problems for polynomials and power series. MSc thesis, Massachusetts Institute of Technology Cambridge. (Cited on page 229).Google Scholar
Shapiro, Joel H. 1977. Remarks on F-spaces of analytic functions. Pages 107124. Lecture Notes in Math., Vol. 604 of: Banach spaces of analytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976). Berlin: Springer. (Cited on page 314).Google Scholar
Sidon, Simon. 1927. Über einen Satz von Herrn Bohr. Math. Z., 26(1), 731732. (Cited on page 204).Google Scholar
Slepian, David. 1962. The one-sided barrier problem for Gaussian noise. Bell System Tech. J., 41, 463501. (Cited on page 472).Google Scholar
Stein, Elias M. and Shakarchi, Rami. 2005. Real analysis. Princeton Lectures in Analysis, vol. 3. Princeton, NJ: Princeton University Press. Measure theory, integration, and Hilbert spaces. (Cited on page 574).Google Scholar
Szarek, Stanisław. 1976. On the best constants in the Khinchin inequality. Studia Math., 58(2), 197208. (Cited on page 150).Google Scholar
Talagrand, Michel. 1992a. Cotype and (q, 1)-summing norm in a Banach space. Invent. Math., 110(3), 545556. (Cited on page 349).Google Scholar
Talagrand, Michel. 1992b. Cotype of operators from C(K). Invent. Math., 107(1), 140. (Cited on page 349).Google Scholar
Tenenbaum, Gérald. 1995. Introduction to analytic and probabilistic number theory. Cambridge Studies in Advanced Mathematics, vol. 46. Cambridge: Cambridge University Press. Translated from the second French edition (1995) by C. B. Thomas. (Cited on pages 35, 220, 221 and 314).Google Scholar
Titchmarsh, Edward C. 1932. The theory of functions. Oxford: Clarendon Press. (Cited on page 35).Google Scholar
Toeplitz, Otto. 1913. Über eine bei den Dirichletschen Reihen auftretende Aufgabe aus der Theorie der Potenzreihen von unendlichvielen Veränderlichen. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 417–432. (Cited on pages 110 and 150).Google Scholar
Tomczak-Jaegermann, Nicole. 1989. Banach-Mazur distances and finite-dimensional operator ideals. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38. Harlow: Longman Scientific & Technical. (Cited on pages 344, 350 and 467).Google Scholar
Tomić, Miodrag. 1962. Sur un théorème de H. Bohr. Math. Scand., 11, 103106. (Cited on page 204).Google Scholar
Tzafriri, Lior. 1974. On Banach spaces with unconditional bases. Israel J. Math., 17, 8493. (Cited on page 543).Google Scholar
Vukotić, Dragan. 2003. The isoperimetric inequality and a theorem of Hardy and Littlewood. Amer. Math. Monthly, 110(6), 532536. (Cited on page 314).Google Scholar
Weissler, Fred B. 1980. Logarithmic Sobolev inequalities and hypercontractive estimates on the circle. J. Funct. Anal., 37(2), 218234. (Cited on page 204).Google Scholar
Wigert, C. Severin. 1907. Sur l’ordre de grandeur du nombre des diviseurs d’un entier. Ark Mat., 3, 19. (Cited on page 307).Google Scholar
Willard, Stephen. 1970. General topology. Reading, MA: Addison-Wesley. (Cited on page 392).Google Scholar
Xu, Quan Hua. 1990. Convexités uniformes et inégalités de martingales. Math. Ann., 287(2), 193211. (Cited on page 628).Google Scholar
Zorn, Max A. 1945. Gâteaux differentiability and essential boundedness. Duke Math. J., 12, 579583. (Cited on page 409).Google Scholar

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