Nash and log-Sobolev inequalities for hypoelliptic operators

被引：6

作者：

Wang, Feng-Yu ^{[1
,2
,3
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

[3] Beijing Normal Univ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

MANUSCRIPTA MATHEMATICA | 2009年 / 128卷 / 03期

基金：

中国国家自然科学基金;

关键词：

58J65; 58J50;

D O I：

10.1007/s00229-008-0235-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By estimating the intrinsic distance and using known heat kernel upper bounds, the global Nash inequality with exact dimension is established for a class of square fields with algebraic growth induced by vector fields satisfying the Hormander condition. As an application, a sufficient condition is presented for the log-Sobolev inequality to hold. Typical examples for Gruschin type operators and generalized Kohn-Lapacians on Heisenberg groups are provided.

引用

页码：343 / 358

页数：16

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