The properties of generalized John domains in metric spaces

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.

Keywords

• generalized john domain
• uniform domain
• decomposition property
• union
• quasiconvex domain