Poincaré inequalities for Littlewood–Paley operators. (September 2017)

• Record Type: Journal Article
• Authors: Liu, Liguang; Yang, Dachun; Zhang, Liying
• Is Part Of: Nonlinear analysis. Volume 160(2017)
• Page Start: 135
• Page End: 158
• Publication Date: 2017-09
• Subjects: primary 42B25 -- secondary 42B35 30H35; Poincaré inequality -- Littlewood–Paley operator -- BMO space -- Lipschitz space -- Hajłasz–Sobolev space; 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.2017.05.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, the authors prove that the inequalities of Poincaré-type are preserved under the action of the Littlewood–Paley operators. Applications to boundedness of the Littlewood–Paley operators on Lipschitz spaces and Hajłasz–Sobolev spaces are considered.