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arXiv · 2606.29969

Compactness of composition operator on weighted Bergman spaces of the polydisc

Anne Dorval
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Abstract

We study composition operators induced by a smooth symbol between weighted Bergman spaces of the polydisc. We first prove a compactness criterion that only requires knowing what happens on the distinguished boundary. Then we prove simple geometric characterizations of boundedness and compactness on some $A^2_\beta(\mathbb{D}^d)$, particularly for $\beta > d-3$.

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Anne Dorval. 2026-06-29. Compactness of composition operator on weighted Bergman spaces of the polydisc. https://arxiv.org/abs/2606.29969

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