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arXiv · 1311.0400

Some properties of the Riesz potentials in Dunkl analysis

Chokri Abdelkefi·Mongi Rachdi
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Abstract

In Dunkl theory on Rd which generalizes classical Fourier analysis, we study first the behavior at infinity of the Riesz potential of a non compactly supported function. Second, we give for 1<p<=q<infinite, weighted (Lp,Lq) boundedness of the Riesz potentials with sufficient conditions. As application, we prove a weighted generalized Sobolev inequality.

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Chokri Abdelkefi, Mongi Rachdi. 2014-04-15. Some properties of the Riesz potentials in Dunkl analysis. https://arxiv.org/abs/1311.0400

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