A Characterization of Riesz Potential and Its Commutator in Local Complementary Generalized Orlicz–Morrey Spaces

In this paper, we find sufficient conditions on functions ω 1 , ω 2 which ensure the boundedness of Riesz potentials and their commutators with BMO functions from one local complementary generalized Orlicz–Morrey spaces to the spaces . As a consequence of the boundedness of the Riesz potential, we give the boundedness the fractional maximal operator in local complementary generalized Orlicz–Morrey spaces.