Abstract
We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted $L^p$-$L^q$ spaces. As an important example, we investigate transforms with kernel of power type, as for instance the sine, Hankel, or $\mathscr{H}_\alpha$ 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.
Funding Statement
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 Matemàtica, Fundació Ferran Sunyer i Balaguer from Institut d'Estudis Catalans, and the MTM2014-59174-P grant.
Citation
Alberto Debernardi. "Weighted norm inequalities for generalized Fourier-type transforms and applications." Publ. Mat. 64 (1) 3 - 42, 2020. https://doi.org/10.5565/PUBLMAT6412001
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