Resumen de Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents

Yoshihiro Sawano, Tetsu Shimomura

• The target is potential theory in connection with Morrey spaces on general metric measure spaces. The present paper is oritented to investigating Sobolev’s inequality, Trudinger exponential integrability and continuity for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents. A counterexample shows that our results are reasonable. In addition to the example above, what is new about this paper is that everything can be developed once the underlying measure does not charge any point.