English

On John domains in Banach spaces

Complex Variables 2013-09-25 v1

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\psi-John domains and prove a similar result for this class.

Keywords

Cite

@article{arxiv.1309.6159,
  title  = {On John domains in Banach spaces},
  author = {Y. Li and M. Vuorinen and X. Wang},
  journal= {arXiv preprint arXiv:1309.6159},
  year   = {2013}
}

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22pages