On Removability Properties of \(\psi \) -Uniform Domains in Banach Spaces

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• 作者：M. Huang ; M. Vuorinen ; X. Wang
• 关键词：Uniform domain ; \(\psi \) ; Uniform domain ; Removability property ; Quasihyperbolic metric
• 刊名：Complex Analysis and Operator Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：11
• 期：1
• 页码：35-55
• 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

Suppose that E is a real Banach space with dimension at least 2. The main aim of this paper is to show that a domain D in E is a \(\psi \)-uniform domain if and only if \(D\backslash P\) is a \(\psi _1\)-uniform domain, and D is a uniform domain if and only if \(D\backslash P\) also is a uniform domain, whenever P is a countable subset of D satisfying a quasihyperbolic separation condition. This condition requires that the quasihyperbolic distance with respect to D between each pair of distinct points in P has a lower bound greater than or equal to \(\frac{1}{2}\).