Weighted norm inequalities for generalized Fourier-type transforms and applications

Autores: Alberto Debernardi Pinos
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 1, 2020, págs. 3-42
Idioma: inglés
DOI: 10.5565/publicacionsmatematiques.v64i1.362822
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Resumen
- We obtain necessary and suﬃcient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted Lp-Lq spaces. As an important example, we investigate transforms with kernel of power type, as for instance the sine, Hankel, or Hα transforms. The obtained necessary and suﬃcient conditions are given in terms of weights, but not in terms of their decreasing rearrangements, as in several previous investigations.