On Bilipschitz Extensions in Real Banach Spaces
Suppose that E and E' denote real Banach spaces with dimension at least 2, that D≠E and D'≠E' are bounded domains with connected boundaries, that f:D→D' is an M-QH homeomorphism, and that D' is uniform. The main aim of this paper is to prove that f extends to a homeomorphism...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/765685 |
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| _version_ | 1849685486419836928 |
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| author | M. Huang Y. Li |
| author_facet | M. Huang Y. Li |
| author_sort | M. Huang |
| collection | DOAJ |
| description | Suppose that E and E' denote real Banach spaces with dimension at least 2, that D≠E and D'≠E' are bounded domains with connected boundaries, that f:D→D' is an M-QH homeomorphism, and that D' is uniform. The main aim of this paper is to prove that f extends to a homeomorphism f¯:D¯→D¯' and f-∣∂D is bilipschitz if and only if f is bilipschitz in D¯. The answer to some open problems of Väisälä is affirmative under a natural additional condition. |
| format | Article |
| id | doaj-art-bf5492ecb1de42e98d888faa4d89f32b |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bf5492ecb1de42e98d888faa4d89f32b2025-08-20T03:23:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/765685765685On Bilipschitz Extensions in Real Banach SpacesM. Huang0Y. Li1Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, ChinaDepartment of Mathematics, Hunan Normal University, Changsha, Hunan 410081, ChinaSuppose that E and E' denote real Banach spaces with dimension at least 2, that D≠E and D'≠E' are bounded domains with connected boundaries, that f:D→D' is an M-QH homeomorphism, and that D' is uniform. The main aim of this paper is to prove that f extends to a homeomorphism f¯:D¯→D¯' and f-∣∂D is bilipschitz if and only if f is bilipschitz in D¯. The answer to some open problems of Väisälä is affirmative under a natural additional condition.http://dx.doi.org/10.1155/2013/765685 |
| spellingShingle | M. Huang Y. Li On Bilipschitz Extensions in Real Banach Spaces Abstract and Applied Analysis |
| title | On Bilipschitz Extensions in Real Banach Spaces |
| title_full | On Bilipschitz Extensions in Real Banach Spaces |
| title_fullStr | On Bilipschitz Extensions in Real Banach Spaces |
| title_full_unstemmed | On Bilipschitz Extensions in Real Banach Spaces |
| title_short | On Bilipschitz Extensions in Real Banach Spaces |
| title_sort | on bilipschitz extensions in real banach spaces |
| url | http://dx.doi.org/10.1155/2013/765685 |
| work_keys_str_mv | AT mhuang onbilipschitzextensionsinrealbanachspaces AT yli onbilipschitzextensionsinrealbanachspaces |