Essential norms and weak compactness of integral operators between weighted Bergman spaces

Abstract

We consider Volterra-type integration operators $T_g$ between Bergman spaces induced by weights $\omega$ satisfying a doubling property. We derive estimates for the operator norms, essential and weak essential norms of $T_g:A_{\omega }^p\to A_{\omega }^q$, $0<p\le q<\infty$. In particular, the operator $T_g:A_{\omega }^1\to A_{\omega }^1$ is weakly compact if and only if it is compact.

References in corpus (1)

• Embedding theorems for Bergman spaces via harmonic analysis