The Fourier transform in weighted Lorentz spaces

Autores: Gord Sinnamon
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 47, Nº 1, 2003, págs. 3-30
Idioma: inglés
DOI: 10.5565/publmat_47103_01
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Resumen
- 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).