$L^p$ Sobolev mapping properties of the Bergman projections on $n$-dimensional generalized Hartogs triangles
Bull. Korean Math. Soc. 2021 Vol. 58, No. 6, 1355-1375
https://doi.org/10.4134/BKMS.b200764
Published online November 1, 2021
Printed November 30, 2021
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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