The Hardy–Littlewood–Sobolev theorem for Riesz potential generated by Gegenbauer operator

Abstract

In this paper we introduced and studied the maximal function (G-maximal function) and the Riesz potential (G-Riesz potential) generated by Gegenbauer differential operator Gλ=(x2−1)12−λddx(x2−1)λ+12ddx. The Lp,λ boundedness of the G-maximal operator is obtained. Hardy–Littlewood–Sobolev theorem of G-Riesz potential on Lp,λ spaces is established.