Riesz potential and maximal function for Dunkl transform

D. V. Gorbachev; V. I. Ivanov; S. Yu. Tikhonov

paper

Riesz potential and maximal function for Dunkl transform

arXiv:1708.09733

Abstract

We study weighted $(L^{p}, L^{q})$ -boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy-Littlewood-Sobolev type inequality and weighted week $(L^{1}, L^{q})$ estimate. We find a sharp constant in the weighted $L^{p}$ -inequality, generalizing the results of W. Beckner and S. Samko.

25 pages