Trudinger-type inequalities in Musielak–Orlicz spaces over metric measure spaces

Abstract Our aim in this note is to deal with Trudinger-type inequalities for variable Riesz potentials of functions in Musielak–Orlicz spaces over bounded metric measure spaces as an extension of the previous paper by Hurri-Syrjänen and the authors ( Complex Var. Elliptic Equ. 68 (2023), no. 10, 1694–1714). As an application, we prove Trudinger-type inequalities for double phase functionals.