Interpolation on Variable Morrey Spaces and Maximal Operators with Trudinger Exponential Integrability

Abstract

The interpolation structure on variable Morrrey spaces defined on quasi-metric spaces are obtained. We deal with the boundedness of the Hardy -Littlewood maximal operator in non – homogeneous central Harz-Morrey-Oricz spaces. The Trudinger inequality and continuity for Riesz potential of functions on metric measure spaces are discussed. We also discuss Trudinger exponential integrability for Riesz potentials of functions in generalized grand Morrey spaces.