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On the subinvariance of uniform domains in Banach spaces




TekijätHuang M, Vuorinen M, Wang X

KustantajaACADEMIC PRESS INC ELSEVIER SCIENCE

Julkaisuvuosi2013

JournalJournal of Mathematical Analysis and Applications

Tietokannassa oleva lehden nimiJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Lehden akronyymiJ MATH ANAL APPL

Numero sarjassa2

Vuosikerta407

Numero2

Aloitussivu527

Lopetussivu540

Sivujen määrä14

ISSN0022-247X

DOIhttps://doi.org/10.1016/j.jmaa.2013.05.046


Tiivistelmä
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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