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 language | English |
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Pages (from-to) | 1137-1142 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 346 |
Issue number | 21-22 |
DOIs | |
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.