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

Abstract

In this paper we prove the boundedness of the generalized fractional integral operator I_ρ on generalized Campanato spaces with variable growth condition, which is a generalization and improvement of previous results, and then, we establish the boundedness of I_ρ on their bi-preduals. We also prove the boundedness of I_ρ on their preduals by the duality.