Extended solution of Boas' conjecture on Fourier transforms

Elijah Liflyand, Sergey Tikhonov

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32 Scopus citations

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).

Original languageEnglish
Pages (from-to)1137-1142
Number of pages6
JournalComptes Rendus Mathematique
Volume346
Issue number21-22
DOIs
StatePublished - 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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