Riesz potential and maximal function for Dunkl transform

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\mathrm{.}Wefindasharpconstantintheweighted$L^p$-inequality, generalizing the results of W. Beckner and S. Samko.