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

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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 contributionWeighted Paley-Wiener theorem on the Hilbert transform
Original languageFrench
Pages (from-to)1253-1258
Number of pages6
JournalComptes Rendus Mathematique
Issue number23-24
StatePublished - 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: (E. Liflyand), (S. Tikhonov).


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