Logarithmic Sobolev Inequalities for Infinite Dimensional Hormander Type Generators on the Heisenberg Group

被引：17
|
作者：
Inglis, J. [1 ]
Papageorgiou, I. [1 ]
机构：
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England
来源：
POTENTIAL ANALYSIS | 2009年 / 31卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
Logarithmic Sobolev inequality; Heisenberg group; Gibbs measures; Hormander type generators; Infinite dimensions; UNBOUNDED SPIN SYSTEMS; HEAT KERNEL; GRADIENT;
D O I：
10.1007/s11118-009-9126-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Heisenberg group is one of the simplest sub-Riemannian settings in which we can define non-elliptic Hormander type generators. We can then consider coercive inequalities associated to such generators. We prove that a certain class of nontrivial Gibbs measures with quadratic interaction potential on an infinite product of Heisenberg groups satisfy logarithmic Sobolev inequalities.
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页码：79 / 102
页数：24
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