On the dimension of the Bergman space of some Hartogs domains with higher dimensional bases (Q2050607)
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scientific article; zbMATH DE number 7388774
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the dimension of the Bergman space of some Hartogs domains with higher dimensional bases |
scientific article; zbMATH DE number 7388774 |
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On the dimension of the Bergman space of some Hartogs domains with higher dimensional bases (English)
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31 August 2021
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The investigation of the dimension of Bergman spaces is an active problem. There are examples of non-pseudoconex domains for which the corresponding Bergman spaces are finite dimensional. In this paper, the author uses Hörmander's \(L^2\) solution to \(\overline{\partial}\) techniques to give sufficient conditions for infinite dimensionality and triviality of certain Hartogs domains.
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Hartogs domains
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balanced domains
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problem of Wiegerinck
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Ohsawa-Takegoshi extension theorem
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pluripotential theory
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