The Boundedness of the Riesz Potential Operator from Generalized Grand Lebesgue Spaces to Generalized Grand Morrey Spaces

We introduce weighted generalized Grand Morrey spaces and prove that the boundedness of linear operators from the generalized Grand Lebesgue spaces to generalized Morrey spaces may be derived from their boundedness from classical weighted Lebesgue spaces into weighted Morrey spaces. As an application we prove a theorem on mapping properties of the Riesz potential operator from weighted generalized Grand Lebesgue spaces to weighted generalized Grand Morrey spaces with Muckenhoupt-Wheeden A(p,q)-weights, under some natural assumptions on the way how we generalize grand spaces.