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Weighted Fourier Transform Inequalities via Mixed Norm Hausdorff-Young Inequalities
Published online by Cambridge University Press: 20 November 2018
Abstract
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Wiener-Lorentz amalgam spaces are introduced and some of their interpolation theoretic properties are discussed. We prove Hausdorff-Young theorems for these spaces unifying and extending Hunt's Hausdorff-Young theorem for Lorentz spaces and Holland's theorem for amalgam spaces. As consequences we prove weighted norm inequalities for the Fourier transform and show how these inequalities fit into a natural class of weighted Fourier transform estimates
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- Copyright © Canadian Mathematical Society 1994
References
[AH]
Aguilera, N. and Harboure, E., In search of weighted norm inequalities for the Fourier transform, Pacific J. Math.
104(1983), 1–14.Google Scholar
[B]
Benedetto, J., Uncertainty principle inequalities and spectrum estimation. In: Fourier Analysis and Applications, NATO-ASI Series C 315, (eds Byrnes, J.), Kluwer Publisher, The Netherlands, 1990, 143–182.Google Scholar
[BH]
Benedetto, J. and Heinig, H., Weighted Hardy spaces and the Laplace transform, Lecture Notes in Math. 992, Springer-Verlag, 1983, 240–277.Google Scholar
[BHJ]
Benedetto, J., Heinig, H. and Johnson, R., Weighted Hardy spaces and the Laplace transform II, Math. Nachr.
132(1987), 29–55.Google Scholar
[BL]
Benedetto, J. and Lakey, J., The definition of the Fourier transform for weighted norm inequalities, J. Funct. Anal., to appear.Google Scholar
[BD]
Bertrandias, J.-P. and Dupuis, C., Transformation de Fourier sur les espaces F ﹛IP ), Ann. Inst. Fourier 29(1979), 189–206.Google Scholar
[BJS]
Bloom, S., Jurkat, W. B. and Sampson, G., Two weighted (LP ,Lq) estimates for the Fourier transform, preprint.Google Scholar
[BB]
Butzer, P. L. and Berens, H., Semi-groups of Operators and Approximation, Springer-Verlag, Berlin- Heidelberg-New York, 1967.Google Scholar
[CD]
Chang, Y. and Davis, K., Lectures on Bochner-Riesz Means, London Math Soc. Lecture Notes Series 114, Cambridge University Press, 1987.Google Scholar
[Fl]
Feichtinger, H., Generalized amalgams, with applications to the Fourier transform, preprint.Google Scholar
[F2]
Feichtinger, H., Banach spaces of distributions of Wiener's type and interpolation. In: Functional Analysis and Approximation, (eds. P. Butzer, B. Sz. Nagy, and E. Gôrlich), ISNM 69, Birkhauser-Verlag, Basel-Boston- Stuttgart, 1981,153-165.Google Scholar
[FI]
Flett, T. M., On a theorem of Pitt, Bull. London Math. Soc. (2)
7(1973), 376–384.Google Scholar
[Fo]
Fournier, J. J. F., On the Hausdorjf-Young theorem for amalgams, Monatsh. Math.
95(1983), 117–135.Google Scholar
[FS]
Fournier, J. J. F. and J. Stewart, Amalgams of If andlq, Bull. Amer. Math. Soc.
13(1985), 1–21.Google Scholar
[H]
Heinig, H., Weighted norm inequalities for classes of operators, Indiana Univ. Math. J. (4)
33(1984), 573–583.Google Scholar
[Hi]
Hirschman, I.I. Jr., Multiplier transformations II, Duke Math. J.
28(1961), 45–56.Google Scholar
[Ho]
Holland, F., Harmonic analysis on amalgams of LP and lq, J. London Math. Soc. (2)
10(1975), 295–305.Google Scholar
[J]
Johnson, R., Recent results on weighted inequalities for the Fourier transform. In: Seminar Analysis of the Karl-WeierstraB-Institute 1986/87,Teubner-texte zurMath., bd. 106, (eds. Schulze, B., Triebel, H.), Teubner, Leipzig, 1988, 287–296.Google Scholar
[JS1]
Jurkat, W. and Sampson, G., On rearrangement and weight inequalities for the Fourier transform, Indiana Univ. Math. J.
33(1984), 257–270.Google Scholar
[JS2]
Jurkat, W. and Sampson, G., On maximal rearrangement inequalities for the Fourier transform, Trans. Amer. Math. Soc. (2)
282(1984), 625–643.Google Scholar
[K]
Kenig, C., Restriction theorems, Carleman estimates, uniform Sobolev inequalities and unique continuation. In: Harmonic Analysis and Partial Differential Equations, Proceedings of Conf. at El Escorial, Lecture Notes in Math 1384, (ed. Garcia Cuerva, J.), Springer-Verlag, 1989, 69–90.Google Scholar
[KS]
Kerman, R. and Sawyer, E., Weighted norm inequalities for potentials with applications to Schrodinger
operators, Fourier transforms, and Carleson measures, Bull. Amer. Math. Soc. (1985), 12112–116.Google Scholar
[LI]
Lakey, J., Trace inequalities, maximal inequalities, and weighted Fourier transform estimates, submitted.Google Scholar
[L2]
Lakey, J., Weighted norm inequalities for the Fourier transform, Ph.D. Thesis, University of Maryland, College Park, 1991.Google Scholar
[Ml]
Muckenhoupt, B., A note on two weight function conditions for a Fourier transform norm inequality, Proc. Amer. Math. Soc. (1) 88(1983), 97–100.Google Scholar
[M2]
Muckenhoupt, B., Weighted norm inequalities for the Fourier transform, Trans. Amer. Math. Soc. (1983), 276729-742.Google Scholar
[R]
Rooney, P. G., GeneralizedHp-spaces and the Laplace transform. In: Proc. Conf. Oberwolfach, Birkhauser, Basel, 1968, 146–156.Google Scholar
[S]
Sagher, Y., Real interpolation with weights, Indiana Univ. Math. J.
30(1981), 113–121.Google Scholar
[St]
Stein, E., Interpolation of linear operators, Trans. Amer. Math. Soc.
83(1956), 482–492.Google Scholar
[SW]
Stein, E. and Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton U. Press, Princeton, N. J., 1971.Google Scholar
[T]
Titchmarsh, E., Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1962.Google Scholar
[Tr]
Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam- New York-Oxford, 1978.Google Scholar
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