Version avec poids du théorème de Paley-Wiener sur la transformée de Hilbert

Elijah Liflyand; Sergey Tikhonov

doi:10.1016/j.crma.2010.10.028

Version avec poids du théorème de Paley-Wiener sur la transformée de Hilbert

Translated title of the contribution: Weighted Paley-Wiener theorem on the Hilbert transform

Elijah Liflyand, Sergey Tikhonov

Department of Mathematics

ICREA

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

14 Scopus citations

Abstract

We prove weighted analogues of the Paley-Wiener theorem on integrability of the Hilbert transform of an integrable odd function which is monotone on R+ This extends Hardy-Littlewood's and Flett's results to the case p=1 under the assumption of (general) monotonicity for an even/odd function.

Translated title of the contribution	Weighted Paley-Wiener theorem on the Hilbert transform
Original language	French
Pages (from-to)	1253-1258
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	348
Issue number	23-24
DOIs	https://doi.org/10.1016/j.crma.2010.10.028
State	Published - Dec 2010

Bibliographical note

Funding Information:
✩ The research was partially supported by the MTM 2008-05561-C02-02, 2009 SGR 1303, RFFI 09-01-00175, NSH-3252.2010.1, and ESF Network Programme HCAA. E-mail addresses: [email protected] (E. Liflyand), [email protected] (S. Tikhonov).

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10.1016/j.crma.2010.10.028

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author = "Elijah Liflyand and Sergey Tikhonov",

note = "Funding Information: ✩ The research was partially supported by the MTM 2008-05561-C02-02, 2009 SGR 1303, RFFI 09-01-00175, NSH-3252.2010.1, and ESF Network Programme HCAA. E-mail addresses: [email protected] (E. Liflyand), [email protected] (S. Tikhonov).",

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AB - We prove weighted analogues of the Paley-Wiener theorem on integrability of the Hilbert transform of an integrable odd function which is monotone on R+ This extends Hardy-Littlewood's and Flett's results to the case p=1 under the assumption of (general) monotonicity for an even/odd function.

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Version avec poids du théorème de Paley-Wiener sur la transformée de Hilbert

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