Weighted norm inequalities for generalized Fourier-type transforms and applications
Debernardi Pinos, Alberto (Bar-Ilan University (Ramat-Gan, Israel). Department of Mathematics)

Date:	2020
Abstract:	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.
Note:	This research was partially funded by the ERC starting grant No. 713927, the ISF grant No. 447/16, the CERCA Programme of the Generalitat de Catalunya, Centre de Recerca Matemàticaca, Fundació Ferran Sunyer i Balaguer from Institut d'Estudis Catalans, and the MTM2014-59174-P grant.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Weighted norm inequalities ; Weighted Lebesgue spaces ; Fourier-type transforms
Published in:	Publicacions matemàtiques, Vol. 64 Núm. 1 (2020) , p. 3-42, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/362822
DOI: 10.5565/PUBLMAT6412001

40 p, 533.6 KB

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