Continuity of Generalized Riesz Potentials for Double Phase Functionals with Variable Exponents over Metric Measure Spaces

Abstract

Our aim in this paper is to deal with the continuity of generalized Riesz potentials $I_{\rho,\tau} f$ of functions in Morrey spaces $L^{\Phi,\nu(\cdot),\kappa}(X)$ of double phase functionals with variable exponents over bounded non-doubling metric measure spaces. What is new in this paper is that $\rho$ depends on $x \in X$.