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Sobolev regularity of the Bergman projection on a class of singular Reinhardt domains

Part of: Holomorphic functions of several complex variables Integral, integro-differential, and pseudodifferential operators

Published online by Cambridge University Press:  22 September 2025

Shuo Zhang
Shuo Zhang*
Affiliation:
College of Science, Tianjin University of Technology , Tianjin 300384, China
*
e-mail: zs.math@alumni.sjtu.edu.cn
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Abstract

In this article, we study the $L^p$ Sobolev regularity of the Bergman projection on monomial polyhedra, which are a wide class of bounded singular Reinhardt domains defined as sublevel sets of holomorphic monomials. This work generalizes the previous results of Sobolev regularity of the Bergman projection on various special singular Reinhardt domains.

Keywords

Sobolev regularityBergman projectionmonomial polyhedra

MSC classification

Primary: 32A36: Bergman spaces 32A25: Integral representations; canonical kernels (Szegő, Bergman, etc.)
Secondary: 47G10: Integral operators

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 17
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12401102 and 12271350) and the Natural Science Foundation of Tianjin Municipality (Grant No. 24JCQNJC00410).

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