Bulletin of the
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Bull. Korean Math. Soc. 2021; 58(6): 1355-1375

Online first article November 1, 2021      Printed November 30, 2021

https://doi.org/10.4134/BKMS.b200764

Copyright © The Korean Mathematical Society.

$L^p$ Sobolev mapping properties of the Bergman projections on $n$-dimensional generalized Hartogs triangles

Shuo Zhang

Tianjin University of Technology

Abstract

The $n$-dimensional generalized Hartogs triangles $\mathbb{H}_{\textbf{p}}^n$ with $n\geq2$ and $\textbf{p}:=(p_1,\ldots,p_n)\in(\mathbb{R}^+)^n$ are the domains defined by $$\mathbb{H}_{\textbf{p}}^n:=\{z=(z_1,\ldots,z_n)\in\mathbb{C}^n:|z_1|^{p_1}<\cdots<|z_n|^{p_n}<1\}.$$ In this paper, we study the $L^p$ Sobolev mapping properties for the \linebreak Bergman projections on the $n$-dimensional generalized Hartogs triangles $\mathbb{H}_{\textbf{p}}^n$, which can be viewed as a continuation of the work by S. Zhang in \cite{Zhang1} and a higher-dimensional generalization of the work by L. D. Edholm and J. D. McNeal in \cite{Edh3}.

Keywords: Bergman projection, generalized Hartogs triangles, $L^p$ Sobolev mapping property

MSC numbers: Primary 32A36, 32A25, 32W05

Supported by: http://bkms.kms.or.kr/journal/view.html?doi=10.4134/BKMS.b200764

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