Some properties of the Riesz potentials in Dunkl analysis

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.

22 pages. arXiv admin note: text overlap with arXiv:1301.6267, arXiv:1305.4394, arXiv:1208.5034