A1 Refereed original research article in a scientific journal
On the subinvariance of uniform domains in Banach spaces
Authors: Huang M, Vuorinen M, Wang X
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2013
Journal: Journal of Mathematical Analysis and Applications
Journal name in source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Journal acronym: J MATH ANAL APPL
Number in series: 2
Volume: 407
Issue: 2
First page : 527
Last page: 540
Number of pages: 14
ISSN: 0022-247X
DOI: https://doi.org/10.1016/j.jmaa.2013.05.046
Abstract
Suppose that E and E' denote real Banach spaces with dimension at least 2, that D subset of E and D' subset of 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 (D-1) of every uniform subdomain D-1 in D under f is still uniform. This result answers an open problem of Vaisala in the affirmative. (C) 2013 Elsevier Inc. All rights reserved.
Suppose that E and E' denote real Banach spaces with dimension at least 2, that D subset of E and D' subset of 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 (D-1) of every uniform subdomain D-1 in D under f is still uniform. This result answers an open problem of Vaisala in the affirmative. (C) 2013 Elsevier Inc. All rights reserved.
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