Reverse Poincare inequalities, isoperimetry, and Riesz transforms in Carnot groups

被引：19

作者：

Baudoin, Fabrice ^{[1
]}

Bonnefont, Michel ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Univ Bordeaux 1, Inst Math Bordeaux, F-33405 Talence, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 131卷

关键词：

Carnot groups; Poincare inequalities; HEAT KERNEL;

D O I：

10.1016/j.na.2015.10.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an optimal reverse Poincare inequality for the heat semigroup generated by the sub-Laplacian on a Carnot group of any step. As an application we give new proofs of the isoperimetric inequality and of the boundedness of the Riesz transform in Carnot groups. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：48 / 59

页数：12

共 13 条

[1]

[Anonymous], 1992, Analysis and Geometry on Groups

[2]

[Anonymous], COMM ANAL GEOM

[3]

[Anonymous], ASTERISQUE

[4] Analysis and geometry of Markov diffusion operators [J].