Extended solution of Boas' conjecture on Fourier transforms

Elijah Liflyand; Sergey Tikhonov

doi:10.1016/j.crma.2008.07.029

Extended solution of Boas' conjecture on Fourier transforms

Elijah Liflyand, Sergey Tikhonov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

Weighted L_p → L_q Fourier inequalities are studied. We prove Boas' conjecture on integrability with power weights of the Fourier transform. One-dimensional as well as multidimensional versions (for radial functions) are obtained for general monotone functions. To cite this article: E. Liflyand, S. Tikhonov, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original language	English
Pages (from-to)	1137-1142
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	346
Issue number	21-22
DOIs	https://doi.org/10.1016/j.crma.2008.07.029
State	Published - Nov 2008

Bibliographical note

Funding Information:
The authors gratefully acknowledge the support of the Gelbart Research Institute for Mathematical Sciences at Bar-Ilan University, Scuola Normale Superiore, the RFFI grants 06-01-00268 and 08-01-00302 and the grant NSH-2787.2008.1. We thank Fulvio Ricci for stimulating discussions.

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abstract = "Weighted Lp → Lq Fourier inequalities are studied. We prove Boas' conjecture on integrability with power weights of the Fourier transform. One-dimensional as well as multidimensional versions (for radial functions) are obtained for general monotone functions. To cite this article: E. Liflyand, S. Tikhonov, C. R. Acad. Sci. Paris, Ser. I 346 (2008).",

author = "Elijah Liflyand and Sergey Tikhonov",

note = "Funding Information: The authors gratefully acknowledge the support of the Gelbart Research Institute for Mathematical Sciences at Bar-Ilan University, Scuola Normale Superiore, the RFFI grants 06-01-00268 and 08-01-00302 and the grant NSH-2787.2008.1. We thank Fulvio Ricci for stimulating discussions.",

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N2 - Weighted Lp → Lq Fourier inequalities are studied. We prove Boas' conjecture on integrability with power weights of the Fourier transform. One-dimensional as well as multidimensional versions (for radial functions) are obtained for general monotone functions. To cite this article: E. Liflyand, S. Tikhonov, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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Extended solution of Boas' conjecture on Fourier transforms

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