On the dimension of the Bergman space of some Hartogs domains with higher dimensional bases
type: Item
instance of: scholarly article
title: On the dimension of the Bergman space of some Hartogs domains with higher dimensional bases
zbMATH Open document ID: 1482.32006
author: Blake J. Boudreaux
published in: The Journal of Geometric Analysis
publication date: 2021-08-31T00:00:00Z
review text: 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.
reviewed by: Yunus E. Zeytuncu
Mathematics Subject Classification ID: 32A36
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 7388774
zbMATH Keywords: Hartogs domains
zbMATH Keywords: balanced domains
zbMATH Keywords: problem of Wiegerinck
zbMATH Keywords: Ohsawa-Takegoshi extension theorem
zbMATH Keywords: pluripotential theory
MaRDI profile type: Publication
full work available at URL: s12220-020-00557-1
OpenAlex ID: W3099451733
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DOI: 10.1007/S12220-020-00557-1
description: scientific article; zbMATH DE number 7388774