A note on an inequality of Bourgain and Brezis. (March 2016)

• Record Type: Journal Article
• Authors: Zhang, Zhibing
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 74
• Page End: 78
• Publication Date: 2016-03
• Subjects: 26D15 -- 46E35; Divergence-free -- Gaffney-type inequality -- L1 vector fields; 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.2015.11.027
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this note, we give a new and elementary approach to an inequality of Bourgain and Brezis (2007) for L 1 vector fields, avoid using the Littlewood–Paley decomposition that Bourgain and Brezis used. And we also give an equivalent version of the inequality. Highlights: A new and elementary proof to an inequality of Bourgain and Brezis is given. Avoid using the Littlewood–Paley decomposition. An equivalent version of the inequality is given.