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

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

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