Weighted Fourier inequalities: Boas' conjecture in ℝn

D. Gorbachev, E. Liflyand, S. Tikhonov

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29 Scopus citations


Weighted Lp(ℝn) → Lq(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 languageEnglish
Pages (from-to)99-120
Number of pages22
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - 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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