Some properties of the Riesz potentials in Dunkl analysis

Published 2 Nov 2013 in math.FA | (1311.0400v4)

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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