Harmonic Analysis
Extended solution of Boas' conjecture on Fourier transforms
Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1137-1142.

Weighted LpLq 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.

On étudie des inégalités LpLq à poids pour des transformées de Fourier, en particulier on formule une conjecture de Boas traduisant une intégrabilité pour des fonctions dans le cas où le poids est une puissance lorsque l'une des fonctions est monotone et p=q. Nous donnons des versions unidimensionnelles et multidimensionnelles (dans le cas de fonctions radiales) pour pq ou pq et pour une classe définie de fonctions généralement monotones.

Published online:
DOI: 10.1016/j.crma.2008.07.029
Liflyand, Elijah 1; Tikhonov, Sergey 2, 3

1 Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
2 Scuola Normale Superiore, 56126 Pisa, Italy
3 ICREA, Passeig Lluís Companys, 23, 08010 Barcelona, Spain
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     title = {Extended solution of {Boas'} conjecture on {Fourier} transforms},
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Liflyand, Elijah; Tikhonov, Sergey. Extended solution of Boas' conjecture on Fourier transforms. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1137-1142. doi : 10.1016/j.crma.2008.07.029. http://www.numdam.org/articles/10.1016/j.crma.2008.07.029/

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