Weighted Fourier inequalities: Boas' conjecture in ℝn

D. Gorbachev; E. Liflyand; S. Tikhonov

doi:10.1007/s11854-011-0013-z

Weighted Fourier inequalities: Boas' conjecture in ℝⁿ

D. Gorbachev, E. Liflyand, S. Tikhonov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

Weighted L^p(ℝⁿ) → L^q(ℝⁿ) Fourier inequalities are studied. We prove Pitt-Boas type results on integrability with power weights of the Fourier transform of a radial function. Extensions to general weights are also given.

Original language	English
Pages (from-to)	99-120
Number of pages	22
Journal	Journal d'Analyse Mathematique
Volume	114
Issue number	1
DOIs	https://doi.org/10.1007/s11854-011-0013-z
State	Published - Sep 2011

Bibliographical note

Funding Information:
∗This research was supported by the Centre de Recerca Matemàtica in Barcelona, the Mathema-tisches Forschungsinstitut Oberwolfach, and by the RFFI 09-01-00175, RFFI 10-01-00564, NSH-3252.2010.1, MTM 2008-05561-C02-02, and 2009 SGR 1303.

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Weighted Fourier inequalities: Boas' conjecture in ℝⁿ

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