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

被引：0
|
作者：
S. K. Vodop’yanov
N. A. Evseev
机构：
[1] Russian Academy of Science,Sobolev Institute of Mathematics, Siberian Branch
[2] Novosibirsk State University,undefined
来源：
Doklady Mathematics | 2015年 / 92卷
关键词：
Sobolev Space; Composition Operator; Hausdorff Dimension; DOKLADY Mathematic; Carnot Group;
D O I：
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中图分类号：
学科分类号：
摘要：
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.
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页码：532 / 536
页数：4
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