Hilbert matrix operator on Bergman-type spaces

Abstract

In this talk, we consider the boundedness of the Hilbert matrix operator on generalized mixed norm spaces and provide a complete characterization expressed by a simple condition in relation to the given parameters. This leads to the characterization of the boundedness of the Hilbert matrix on the weighted Bergman spaces and weighted Dirichlet spaces. We also discuss the question of determining the exact norm of the Hilbert matrix on the weighted Bergman spaces.