On the subinvariance of uniform domains in Banach spaces
On the subinvariance of uniform domains in Banach spaces
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DOI：
10.1016/j.jmaa.2013.05.046
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发表时间：
2012-09
影响因子：
1.3
通讯作者：
Manzi Huang;Xiantao Wang;M. Vuorinen
中科院分区：
文献类型：
--
作者：
Manzi Huang;Xiantao Wang;M. Vuorinen
Suppose that E and E′denote real Banach spaces with dimension at least 2, that D⊂E and D′⊂E′are domains, and that f:D→D′is a homeomorphism. In this paper, we prove the following subinvariance property for the class of uniform domains: suppose that f is a freely quasiconformal mapping and that D′is uniform. Then the image f(D1) of every uniform subdomain D1in D under f is still uniform. This result answers an open problem of Väisälä in the affirmative.
