Characterizations for the Riesz potential and its commutators on generalized Orlicz-Morrey spaces

Abstract

In the present paper, we shall give a characterization for the Spanne and Adams type boundedness of the Riesz potential and its commutators on the generalized Orlicz-Morrey spaces, respectively. Also we give criteria for the weak versions of Spanne and Adams type boundedness of the Riesz potential on the generalized Orlicz-Morrey spaces. In all the cases the conditions for the boundedness are given in terms of Zygmund type integral inequalities involving the Young function Phi (u) and the function phi(x, r) defining the space.