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.

引用

页码：79 / 102

页数：24

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