Littlewood–Paley functions and Sobolev spaces. (July 2019) - Chen, Jiecheng; Fan, Dashan; Zhao, Fayou
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.