The Bergman kernel function of some Reinhardt domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Bergman kernel function of some Reinhardt domains

Authors:	Sheng Gong Xuean Zheng

Institution:	Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China - Department of Mathematics, University of California, San Diego, La Jolla, California 92093 Xuean Zheng ; Department of Mathematics, Anhui University, Hefei, Anhui, 230039, People's Republic of China

Abstract:	The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points $(z,\bar z)$ . Let be the Reinhardt domain $\begin{displaymath}D=\left\{ z\in\mathbf C^n\,\|\,\\|z\\|_\alpha=\sum_{j=1}^n\|z_j\|^{2/\al_j}<1\right\} \end{displaymath}$ where $\al_j>0$ , $j=1,2,\dots, n$ ; and let $K(z,\bar w)$ be the Bergman kernel function of . Then there exist two positive constants and and a function such that $\begin{displaymath}mF(z,\bar z) \le K(z,\bar z)\le MF(z,\bar z) \end{displaymath}$ holds for every $z\in D$ . Here $\begin{displaymath}F(z,\bar z)=(-r(z))^{-n-1} \prod_{j=1}^n (-r(z)+\|z_j\|^{2/\al_j})^{1-\al_j} \end{displaymath}$ and $r(z)=\\|z\\|_\alpha-1$ is the defining function for . The constants and depend only on $\alpha=(\al_1,\dots, \al_n)$ and , not on .

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