Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces

Abstract

We prove a generalized Trudinger's inequality for Riesz potentials of Musielak-Orlicz functions defined in a bounded metric measure space. As a corollary we obtain Trudinger's inequality for double phase functionals , where and satisfy log-Hölder conditions and is non-negative, bounded and Hölder continuous.