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The Fourier transform in weighted Lorentz spaces
Sinnamon, Gord

Data: 2003
Resum: 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).
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Fourier transform ; Weights ; Lorentz space
Publicat a: Publicacions matematiques, V. 47 N. 1 (2003) , p. 3-29, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_47103_01

27 p, 224.2 KB

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