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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*
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

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

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