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Lp SOBOLEV MAPPING PROPERTIES OF THE BERGMAN PROJECTIONS ON n-DIMENSIONAL GENERALIZED HARTOGS TRIANGLES

Shuo Zhang
대한수학회 (The Korean Mathematical Society)|2021.11|대한수학회보 (Bulletin of the KMS)|제58권 제6호|pp. 1355-1375|DOI 10.4134/BKMS.b200764

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키워드

Bergman projectiongeneralized Hartogs trianglesLp Sobolev mapping property
주제분류수학

초록

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}.

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}.

참고문헌 (26)

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