Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces

Our aim in this paper is to give Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces. The main result is oriented to the outrange of the well-known Adams theorem. MSC: 31B15, 46E35, 26A33. Our aim in this paper is to give Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces. The main result is oriented to the outrange of the well-known Adams theorem. MSC: 31B15, 46E35, 26A33.