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.