Generalized Hilbert matrix operators acting on Bergman spaces

Abstract

In this article we study the generalized Hilbert matrix operator $\hat{I}{“}_{\hat{I}}¼$ acting on the Bergman spaces $A^p$ of the unit disc for $1\le p<\infty$. In particular, we characterize the measures $\hat{I}¼$ for which the operator $\hat{I}{“}_{\hat{I}}¼$ is bounded and we provide estimates of its operator norm. Finally, we also describe when $\hat{I}{“}_{\hat{I}}¼$ is compact by computing its essential norm.