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arXiv · 1812.01928

Weighted norm inequalities for generalized Fourier-type transforms and applications

A. Debernardi
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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.

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A. Debernardi. 2018-12-05. Weighted norm inequalities for generalized Fourier-type transforms and applications. https://arxiv.org/abs/1812.01928

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