Capacities, Green function, and Bergman functions

Using the logarithmic capacity, we give quantitative estimates of the Green function, as well as precise lower bounds of the Bergman kernel for bounded pseudoconvex domains in and the Bergman distance for bounded planar domains. In particular, it is shown that the Bergman kernel satisfies the sharp...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2023-11, Vol.108 (5), p.1930-1953
Main Author: Chen, Bo‐Yong
Format: Article
Language:English
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Summary:Using the logarithmic capacity, we give quantitative estimates of the Green function, as well as precise lower bounds of the Bergman kernel for bounded pseudoconvex domains in and the Bergman distance for bounded planar domains. In particular, it is shown that the Bergman kernel satisfies the sharp estimate if is a bounded pseudoconvex domain with ‐boundary.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12798