Riesz Potential and Fractional Maximal Function

Abstract

In this article, we begin with Riesz potential. We then discuss some properties of the Riesz potential. Finally we discuss a relation of  Riesz Potential with fractional maximal function in the sense that fractional maximal function can be controlled by Riesz potential and the fractional  maximal function maps  the space Lp to Lq whenever the Riesz potential does.