Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings

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• 作者：S. K. Vodop’yanov ; N. A. Evseev
• 关键词：composition operator ; Sobolev space ; quasiconformal mapping ; Carnot group
• 刊名：Siberian Mathematical Journal
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：56
• 期：5
• 页码：789-821
• 全文大小：479 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, Novosibirsk, Russia
  2. Novosibirsk State University, Novosibirsk, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9260

文摘

We prove that a measurable mapping of domains on a Carnot group induces by the corresponding change of variables an isomorphism of the Sobolev spaces whose integrability exponent is equal to the Hausdorff dimension of the group if and only if the mapping coincides with a quasiconformal mapping almost everywhere. Keywords composition operator Sobolev space quasiconformal mapping Carnot group