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
收藏
页码：532 / 536
页数：5
相关论文
共 50 条
12345