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The Fourier transform in weighted Lorentz spaces
Sinnamon, Gord

Date: 2003
Abstract: Necessary conditions and sufficient conditions on weights u and w are given for the Fourier transform F to be bounded as a map between the Lorentz spaces Γq(w) and Λp(u). This may be viewed as a weighted extension of a result of Jodeit and Torchinsky on operators of type (1, ∞) and (2, 2). In the case 0 < p ≤ 2 = q, the necessary and sufficient conditions are equivalent and give a simple weight condition which is equivalent to F : Γ2(w) → Λp(u) and also to F : Γ2(w) → Γp(u).
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió publicada
Subject: Fourier transform ; Weights ; Lorentz space
Published in: Publicacions matemàtiques, V. 47 N. 1 (2003) , p. 3-29, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38064
DOI: 10.5565/PUBLMAT_47103_01


27 p, 224.2 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles

 Record created 2006-03-13, last modified 2022-02-20



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