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Weighted Fourier Transform Inequalities via Mixed Norm Hausdorff-Young Inequalities

Published online by Cambridge University Press:  20 November 2018

Joseph D. Lakey
Joseph D. Lakey*
Affiliation:
Department of Mathematics University of Texas Austin, Texas 78712 U.S.A.
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Abstract

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Wiener-Lorentz amalgam spaces are introduced and some of their interpolation theoretic properties are discussed. We prove Hausdorff-Young theorems for these spaces unifying and extending Hunt's Hausdorff-Young theorem for Lorentz spaces and Holland's theorem for amalgam spaces. As consequences we prove weighted norm inequalities for the Fourier transform and show how these inequalities fit into a natural class of weighted Fourier transform estimates

Keywords

42B46EFourier transforminterpolationweighted norm inequalities
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 586 - 601
Copyright
Copyright © Canadian Mathematical Society 1994

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