Compactness of composition operator on weighted Bergman spaces of the polydisc

Anne Dorval

Compactness of composition operator on weighted Bergman spaces of the polydisc

Functional Analysis 2026-06-29 v1

Authors: Anne Dorval

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 $\beta > d-3$ .

Keywords

composition operators weighted Bergman spaces polydisc compactness boundedness

Cite

@article{arxiv.2606.29969,
  title  = {Compactness of composition operator on weighted Bergman spaces of the polydisc},
  author = {Anne Dorval},
  journal= {arXiv preprint arXiv:2606.29969},
  year   = {2026}
}