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arXiv · 1506.05414

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

Santeri Miihkinen·Pekka Nieminen·Wen Xu
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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.

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Santeri Miihkinen, Pekka Nieminen, Wen Xu. 2015-06-17. Essential norms and weak compactness of integral operators between weighted Bergman spaces. https://arxiv.org/abs/1506.05414

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