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

TL;DR

This paper investigates the properties of Volterra-type integral operators between weighted Bergman spaces, providing estimates for their norms and characterizing weak compactness in terms of compactness.

Contribution

It offers new estimates for operator norms and essential norms, and characterizes weak compactness of integral operators on weighted Bergman spaces.

Findings

Operator norms are estimated in terms of weights and functions.

Weak compactness coincides with compactness for operators on A_ω^1.

Characterization of essential and weak essential norms for these operators.

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 $T_g: A_\omega^p \to A_\omega^q$, $0<p\leq q<\infty$. In particular, the operator $T_g: A_\omega^1\to A_\omega^1$ is weakly compact if and only if it is compact.