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

被引：7

作者：

Vodop'yanov, S. K. ^{[1
,2
]}

Evseev, N. A. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

来源：

DOKLADY MATHEMATICS | 2015年 / 92卷 / 02期

关键词：

DIFFERENTIABILITY;

D O I：

10.1134/S1064562415050117

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：532 / 536

页数：5

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