Young Inequalities in Variable Lebesgue Spaces and Riesz Potential with Maximal Operators in Generalized Orlicz Spaces

Abstract

The Trudinger inequality for Riesz potentials of functions in Musielak-Orlicz spaces, in generalizes Orlicz spaces and Sobolev embedding on generalized Lebesgue and Sobolev spaces are studied. We determine the boundedness of the maximal functions and operators with approximate identities and Sobolev inequalities on Musielak-Orlicz-Morrey spaces. Also the boundedness of the classical operators, local-to-global result and fractional operators in weighted and variable exponent spaces are considered. The Sobolev inequalities and embedding, mean continuity type results, type Young inequalities and regularity for double phase for Orlicz and certain Sobolev spaces are given and characterized.