Density in weighted Bergman spaces and Bergman completeness of Hartogs domains
Abstract
We study the density of functions which are holomorphic in a neighbourhood of the closure $\overline{\Omega}$ of a bounded non-smooth pseudoconvex domain $\Omega$, in the Bergman space $ H^2(\Omega ,\varphi)$ with a plurisubharmonic weight $\varphi$. As an application, we show that the Hartogs domain $$ \Omega _\alpha : = \{(z,w) \in D\times \C: |w|< \delta^\alpha_D(z) \}, \ \ \ \alpha>0, $$ where $D\subset \subset \C$ and $\delta_D$ denotes the boundary distance, is Bergman complete if and only if every boundary point of $D$ is non-isolated.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.16494
- arXiv:
- arXiv:2402.16494
- Bibcode:
- 2024arXiv240216494C
- Keywords:
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- Mathematics - Complex Variables
- E-Print:
- 23pages