[Solutions prolongées de la conjecture de Boas sur les transformées de Fourier]
On étudie des inégalités 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 . Nous donnons des versions unidimensionnelles et multidimensionnelles (dans le cas de fonctions radiales) pour ou et pour une classe définie de fonctions généralement monotones.
Weighted 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.
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@article{CRMATH_2008__346_21-22_1137_0,
author = {Liflyand, Elijah and Tikhonov, Sergey},
title = {Extended solution of {Boas'} conjecture on {Fourier} transforms},
journal = {Comptes Rendus. Math\'ematique},
pages = {1137--1142},
publisher = {Elsevier},
volume = {346},
number = {21-22},
year = {2008},
doi = {10.1016/j.crma.2008.07.029},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.07.029/}
}
TY - JOUR AU - Liflyand, Elijah AU - Tikhonov, Sergey TI - Extended solution of Boas' conjecture on Fourier transforms JO - Comptes Rendus. Mathématique PY - 2008 SP - 1137 EP - 1142 VL - 346 IS - 21-22 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.07.029/ DO - 10.1016/j.crma.2008.07.029 LA - en ID - CRMATH_2008__346_21-22_1137_0 ER -
%0 Journal Article %A Liflyand, Elijah %A Tikhonov, Sergey %T Extended solution of Boas' conjecture on Fourier transforms %J Comptes Rendus. Mathématique %D 2008 %P 1137-1142 %V 346 %N 21-22 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.07.029/ %R 10.1016/j.crma.2008.07.029 %G en %F CRMATH_2008__346_21-22_1137_0
Liflyand, Elijah; Tikhonov, Sergey. Extended solution of Boas' conjecture on Fourier transforms. Comptes Rendus. Mathématique, Tome 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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