The properties of generalized John domains in metric spaces

Hongjun Liu; Fang Yan; Ling Xia; Hongjun Liu; Fang Yan; Ling Xia

doi:10.3934/math.2024767

AIMS Mathematics

2024, Volume 9, Issue 6: 15875-15890. doi: 10.3934/math.2024767

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Research article

The properties of generalized John domains in metric spaces

School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, China

Received: 19 February 2024 Revised: 27 March 2024 Accepted: 18 April 2024 Published: 06 May 2024
MSC : 30C20, 30C65

In this paper, we studied the properties of generalized John domains in metric space. We prove that a domain $ D $ is a $ \varphi $-John domain if, and only if, $ D\backslash P $ is a $ \varphi' $-John domain, where $ P $ is a subset of $ D $ containing finitely many points of $ D $. Meanwhile, we also showed that the union of $ \varphi $-John domains is a $ \varphi'' $-John domain in metric space.
- Generalized John domain,
- uniform domain,
- decomposition property,
- union,
- quasiconvex domain
Citation: Hongjun Liu, Fang Yan, Ling Xia. The properties of generalized John domains in metric spaces[J]. AIMS Mathematics, 2024, 9(6): 15875-15890. doi: 10.3934/math.2024767

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Abstract

In this paper, we studied the properties of generalized John domains in metric space. We prove that a domain $ D $ is a $ \varphi $-John domain if, and only if, $ D\backslash P $ is a $ \varphi' $-John domain, where $ P $ is a subset of $ D $ containing finitely many points of $ D $. Meanwhile, we also showed that the union of $ \varphi $-John domains is a $ \varphi'' $-John domain in metric space.

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