Weighted norm inequalities for generalized Fourier-type transforms and applications

2018/12/05 by Debernardi, A. · 1 citation
#42A38 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.01928

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 \mathscrH_α 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.

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• Shifted Pitt and uncertainty inequalities on Riemannian symmetric spaces of noncompact type

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