Boundedness of the Generalized Fractional Integral Operators on Generalized Morrey Spaces over Metric Measure Spaces

Abstract

Our aim in this paper is to deal with the boundedness of the generalized fractional integral operators on generalized Morrey spaces $L_{p,\varphi ;2}(X;\mu )$ over metric measure spaces. We also discuss a necessary condition for the boundedness of the generalized fractional integral operators. As applications, we establish new results for the predual spaces.