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Weighted Fourier Transform Inequalities via Mixed Norm Hausdorff-Young Inequalities
Published online by Cambridge University Press: 20 November 2018
Abstract
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
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- Copyright © Canadian Mathematical Society 1994