Generalized Hilbert matrix operators acting on Bergman spaces

Abstract

In this article we study the generalized Hilbert matrix operator ${\Gamma }_{\mu }$ acting on the Bergman spaces $A^p$ of the unit disc for $1\le p<\infty$. In particular, we characterize the measures $\mu$ for which the operator ${\Gamma }_{\mu }$ is bounded and we provide estimates of its operator norm. Finally, we also describe when ${\Gamma }_{\mu }$ is compact by computing its essential norm.