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arXiv · 1708.04949

On the $p$-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains

Ronald G. Douglas·Kunyu Guo·Yi Wang
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Abstract

In this paper, we show that under a mild condition, a principal submodule of the Bergman module on a bounded strongly pseudoconvex domain with smooth boundary in $\mathbb{C}^n$ is $p$-essentially normal for all $p>n$. This improves a previous result by the first author and K. Wang, in which it was shown that any polynomial-generated principal submodule of the Bergman module on the unit ball $\mathbb{B}_n$ is $p$-essentially normal for all $p>n$. As a consequence, we show that the submodule of $L_a^2(\mathbb{B}_n)$ consisting of functions vanishing on an analytic subset of pure codimension $1$ is $p$-essentially normal for all $p>n$.

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Ronald G. Douglas, Kunyu Guo, Yi Wang. 2017-08-16. On the $p$-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains. https://arxiv.org/abs/1708.04949

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