On Sobolev-type Inequalities on Morrey Spaces of an Integral Form

Abstract

We prove Sobolev-type inequalities for modified Riesz potentials of functions in Morrey spaces of an integral form over non-doubling metric measure spaces. Our results are new even for the doubling metric measure setting. In particular, our results extend the previous results in Morrey spaces of an integral form in the Euclidean case.