Reverse Poincaré inequalities, isoperimetry, and Riesz transforms in Carnot groups. (January 2016)

• Record Type: Journal Article
• Authors: Baudoin, Fabrice; Bonnefont, Michel
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 48
• Page End: 59
• Publication Date: 2016-01
• Subjects: Carnot groups -- Poincaré inequalities; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.10.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove an optimal reverse Poincaré 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.