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Analysis Seminar – Ryan Berndt, Otterbein University
April 1 @ 11:00 am - 12:00 pm
Title: Two-weight problem for the Fourier transform.
Abstract: We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is connected to an old result of Mahler concerning the the measure of a convex body and its geometric polar being essentially reciprocal. An additional assumption, that the weights must belong to a reverse Hölder class, is used to formulate the sufficient condition.