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.
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This research was supported by the Centre de Recerca Matemàtica in Barcelona, the Mathematisches 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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Gorbachev, D., Liflyand, E. & Tikhonov, S. Weighted Fourier inequalities: Boas’ conjecture in ℝn . JAMA 114, 99–120 (2011). https://doi.org/10.1007/s11854-011-0013-z
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DOI: https://doi.org/10.1007/s11854-011-0013-z