Hardy’s inequalities for Hermite and Laguerre expansions
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- by R. Radha and S. Thangavelu
- Proc. Amer. Math. Soc. 132 (2004), 3525-3536
- DOI: https://doi.org/10.1090/S0002-9939-04-07554-9
- Published electronically: July 12, 2004
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Abstract:
Hardy’s inequalities are proved for higher-dimensional Hermite and special Hermite expansions of functions in Hardy spaces. Inequalities for multiple Laguerre expansions are also deduced.References
- Leonardo Colzani and Giancarlo Travaglini, Hardy-Lorentz spaces and expansions in eigenfunctions of the Laplace-Beltrami operator on compact manifolds, Colloq. Math. 58 (1990), no. 2, 305–315. MR 1060182, DOI 10.4064/cm-58-2-305-315
- Yuichi Kanjin, Hardy’s inequalities for Hermite and Laguerre expansions, Bull. London Math. Soc. 29 (1997), no. 3, 331–337. MR 1435569, DOI 10.1112/S0024609396002627
- Giancarlo Mauceri, Massimo A. Picardello, and Fulvio Ricci, A Hardy space associated with twisted convolution, Adv. in Math. 39 (1981), no. 3, 270–288. MR 614164, DOI 10.1016/0001-8708(81)90004-9
- R. Radha, Hardy-type inequalities, Taiwanese J. Math. 4 (2000), no. 3, 447–456. MR 1779109, DOI 10.11650/twjm/1500407261
- Makoto Satake, Hardy’s inequalities for Laguerre expansions, J. Math. Soc. Japan 52 (2000), no. 1, 17–24. MR 1727203, DOI 10.2969/jmsj/05210017
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
- S. Thangavelu, On regularity of twisted spherical means and special Hermite expansions, Proc. Indian Acad. Sci. Math. Sci. 103 (1993), no. 3, 303–320. MR 1273356, DOI 10.1007/BF02866993
- Sundaram Thangavelu, Lectures on Hermite and Laguerre expansions, Mathematical Notes, vol. 42, Princeton University Press, Princeton, NJ, 1993. With a preface by Robert S. Strichartz. MR 1215939
Bibliographic Information
- R. Radha
- Affiliation: School of Mathematics, Anna University, Chennai - 600 025, India
- Address at time of publication: Department of Mathematics, Indian Institute of Technology, Chennai - 600 036, India
- Email: radharam@annauniv.edu
- S. Thangavelu
- Affiliation: Stat-Math Unit, Indian Statistical Institute, 8th Mile, Mysore Road (R.V. College Post), Bangalore - 560 059, India
- Email: veluma@isibang.ac.in
- Received by editor(s): February 18, 2002
- Received by editor(s) in revised form: October 14, 2002
- Published electronically: July 12, 2004
- Communicated by: Andreas Seeger
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3525-3536
- MSC (2000): Primary 42C10; Secondary 42B30, 42C05, 33C45
- DOI: https://doi.org/10.1090/S0002-9939-04-07554-9
- MathSciNet review: 2084073