Generalized fractional integral operators on Morrey spaces and their bi-preduals

Abstract

In this paper we prove the boundedness of the generalized fractional integral operator \(I_{\rho }\) on generalized Morrey spaces with variable growth condition, which is an improvement of previous results, and then, we establish the boundedness of \(I_{\rho }\) on their bi-preduals. We also prove the boundedness of \(I_{\rho }\) on their preduals by the duality.