Density in weighted Bergman spaces and Bergman completeness of Hartogs domains

Bo-Yong Chen; John Erik Fornæss; Jujie Wu

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arXiv · 2402.16494

Density in weighted Bergman spaces and Bergman completeness of Hartogs domains

Bo-Yong Chen·John Erik Fornæss·Jujie Wu

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Abstract

We study the density of functions which are holomorphic in a neighbourhood of the closure $\overlineΩ$ of a bounded non-smooth pseudoconvex domain $Ω$, in the Bergman space $ H^2(Ω,φ)$ with a plurisubharmonic weight $φ$. As an application, we show that the Hartogs domain $$ Ω_α: = \{(z,w) \in D\times \C: |w|< δ^α_D(z) \}, \ \ \ α>0, $$ where $D\subset \subset \C$ and $δ_D$ denotes the boundary distance, is Bergman complete if and only if every boundary point of $D$ is non-isolated.

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BibTeX RIS

Bo-Yong Chen, John Erik Fornæss, Jujie Wu. 2024-02-26. Density in weighted Bergman spaces and Bergman completeness of Hartogs domains. https://arxiv.org/abs/2402.16494

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