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
收藏
页码：343 / 358
页数：16
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