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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 765685, 9 pages
http://dx.doi.org/10.1155/2013/765685
Research Article

On Bilipschitz Extensions in Real Banach Spaces

Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China

Received 11 October 2012; Accepted 20 February 2013

Academic Editor: Beong In Yun

Copyright © 2013 M. Huang and Y. Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Suppose that and denote real Banach spaces with dimension at least 2, that and are bounded domains with connected boundaries, that is an -QH homeomorphism, and that is uniform. The main aim of this paper is to prove that extends to a homeomorphism and is bilipschitz if and only if is bilipschitz in . The answer to some open problems of Väisälä is affirmative under a natural additional condition.