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arXiv:1311.0400 [math.FA]AbstractReferencesReviewsResources

Some properties of the Riesz potentials in Dunkl analysis

Chokri Abdelkefi, Mongi Rachdi

Published 2013-11-02, updated 2014-04-15Version 4

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.

Comments: 22 pages. arXiv admin note: text overlap with arXiv:1301.6267, arXiv:1305.4394, arXiv:1208.5034
Categories: math.FA
Subjects: 42B10, 46E30, 44A35
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