Weighted Fourier Transform Inequalities via Mixed NormHausdorff-Young Inequalities

Lakey, Joseph D.

Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 586-601

Résumé

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

Détail

DOI : 10.4153/CJM-1994-031-7

Mots-clés : 42B, 46E, Fourier transform, interpolation, weighted norm inequalities

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