Sobolev's inequality in Musielak–Orlicz–Morrey spaces of an integral form

Abstract

AbstractIn this paper, we are concerned with Sobolev's inequality for variable Riesz potentials of functions f in Musielak–Orlicz–Morrey spaces of an integral form over metric measure spaces. As an application and example, we give Sobolev's inequality for double‐phase functionals , where and satisfy log‐Hölder conditions and is non‐negative, bounded and Hölder continuous of order . Further, we obtain the result for Sobolev functions.