On John domains in Banach spaces

Y. Li; M. Vuorinen; X. Wang

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arXiv · 1309.6159

On John domains in Banach spaces

Y. Li·M. Vuorinen·X. Wang

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Abstract

We study the stability of John domains in Banach spaces under removal of a countable set of points. In particular, we prove that the class of John domains is stable in the sense that removing a certain type of closed countable set from the domain yields a new domain which also is a John domain. We apply this result to prove the stability of the inner uniform domains. Finally, we consider a wider class of domains, so called $ψ$-John domains and prove a similar result for this class.

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Y. Li, M. Vuorinen, X. Wang. 2013-09-24. On John domains in Banach spaces. https://arxiv.org/abs/1309.6159

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