Littlewood–Paley functions and Sobolev spaces. (July 2019)

• Record Type: Journal Article
• Authors: Chen, Jiecheng; Fan, Dashan; Zhao, Fayou
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 273
• Page End: 297
• Publication Date: 2019-07
• Subjects: primary 46E35 -- secondary 42B25 42B35; Littlewood–Paley square functions -- Sobolev spaces -- Spherical average -- Ball average -- Bochner–Riesz means; 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.2019.02.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish Littlewood–Paley characterizations of the Sobolev spaces W α, p in Euclidean spaces using several square functions defined via the spherical average, the ball average, the Bochner–Riesz means and some other well known operators. We provide a simple proof so that we are able to extend and improve many results published in recent papers.