Boundary Schwarz Lemma for Holomorphic Self-mappings of Strongly Pseudoconvex Domains
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- 作者：Xieping Wang ; Guangbin Ren
- 关键词：Holomorphic mappings ; Boundary Schwarz lemma ; Carathéodory metric ; Strongly pseudoconvex domains ; Graham’s estimate
- 刊名：Complex Analysis and Operator Theory
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：11
- 期：2
- 页码：345-358
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general; Operator Theory; Analysis;
- 出版者：Springer International Publishing
- ISSN：1661-8262
- 卷排序：11
文摘
In this paper, we generalize a recent work of Liu et al. from the open unit ball \({\mathbb {B}}^n\subset {\mathbb {C}}^n\) to more general bounded strongly pseudoconvex domains with \(C^2\) boundaries. It turns out that part of the main result in this paper is in some certain sense just a part of results in a work of Bracci and Zaitsev. However, the proofs are significantly different: the argument in this paper involves a simple growth estimate for the Carathéodory metric near the boundary of \(C^2\) domains and the well-known Graham’s estimate on the boundary behavior of the Carathéodory metric on strongly pseudoconvex domains, while Bracci and Zaitsev use other arguments.