Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings

被引：0
|
作者：
S. K. Vodop’yanov
N. A. Evseev
机构：
[1] Sobolev Institute of Mathematics,
[2] Novosibirsk State University,undefined
来源：
Siberian Mathematical Journal | 2015年 / 56卷
关键词：
composition operator; Sobolev space; quasiconformal mapping; Carnot group;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：789 / 821
页数：32
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