Isomorphisms of sobolev spaces on carnot groups and metric properties of mappings

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• 作者：S. K. Vodop’yanov ; N. A. Evseev
• 刊名：Doklady Mathematics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：92
• 期：2
• 页码：532-536
• 全文大小：290 KB
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• 作者单位：S. K. Vodop’yanov (1) (2)
  N. A. Evseev (1) (2)
  
  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Science, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia
  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8362

文摘

We study metric properties of measurable mappings on a Carnot group inducing via the change-of-variable formula an isomorphism of Sobolev spaces. We prove that such a mapping can be redefined on a set of measure zero to be quasiconformal or quasi-isometric depending on a relation between the Hausdorff dimension of the group and a summability exponent of the Sobolev space. Original Russian Text ? S.K. Vodop’yanov, N.A. Evseev, 2015, published in Doklady Akademii Nauk, 2015, Vol. 464, No. 2, pp. 131-35.Presented by Academician Yu.G. Reshetnyak February 1, 2015The article was translated by the authors.