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arXiv · 2103.04145

Invariant subspaces of weighted Bergman spaces in infinitely many variables

Hui Dan·Kunyu Guo·Jiaqi Ni
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Abstract

This paper is concerned with polynomially generated multiplier invariant subspaces of the weighted Bergman space $A_{\boldsymbol{\beta}}^2$ in infinitely many variables. We completely classify these invariant subspaces under the unitary equivalence. Our results not only cover cases of both the Hardy space $H^{2}(\mathbb{D}_{2}^{\infty})$ and the Bergman space $A^{2}(\mathbb{D}_{2}^{\infty})$ in infinitely many variables, but also apply in finite-variable setting.

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Hui Dan, Kunyu Guo, Jiaqi Ni. 2021-03-06. Invariant subspaces of weighted Bergman spaces in infinitely many variables. https://arxiv.org/abs/2103.04145

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