On removability properties of $ψ$-uniform domains in Banach spaces

M. Huang; M. Vuorinen; X. Wang

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arXiv · 1206.0128

On removability properties of $ψ$-uniform domains in Banach spaces

M. Huang·M. Vuorinen·X. Wang

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Abstract

Suppose that $E$ denotes a real Banach space with the dimension at least 2. The main aim of this paper is to show that a domain $D$ in $E$ is a $ψ$-uniform domain if and only if $D\backslash P$ is a $ψ_1$-uniform domain, and $D$ is a uniform domain if and only if $D\backslash P$ also is a uniform domain, whenever $P$ is a closed countable subset of $D$ satisfying a quasihyperbolic separation condition. This condition requires that the quasihyperbolic distance (w.r.t. $D$) between each pair of distinct points in $P$ has a lower bound greater than or equal to $\frac{1}{2}$.

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BibTeX RIS

M. Huang, M. Vuorinen, X. Wang. 2013-06-21. On removability properties of $ψ$-uniform domains in Banach spaces. https://arxiv.org/abs/1206.0128

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