Norm of the generalized Hilbert operator on weighted Bergman spaces

Abstract

Several upper bounds as well as one lower bound for the operator norm of the generalized Hilbert operator ${\mathcal{H}}_b$ acting on weighted Bergman spaces $A_{\alpha }^p$ are established. Moreover, under some mild assumptions, we obtain the exact norm of ${\mathcal{H}}_b$ on $A_{\alpha }^p$.

The first draft of this paper was written in 2018. The work in this paper was presented at a conference held at Guangzhou University in July, 2026