Density in weighted Bergman spaces and Bergman completeness of Hartogs domains
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909120236355584 |
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| author | Chen, Bo-Yong Fornæss, John Erik Wu, Jujie |
| author_facet | Chen, Bo-Yong Fornæss, John Erik Wu, Jujie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density in weighted Bergman spaces and Bergman completeness of Hartogs domains Chen, Bo-Yong Fornæss, John Erik Wu, Jujie Complex Variables 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. |
| title | Density in weighted Bergman spaces and Bergman completeness of Hartogs domains |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2402.16494 |