A Study of One-Sided Singular Integral and Function Space via Reproducing Formula

In this paper, we systematically establish the theory of one-sided Hardy spaces, including Littlewood–Paley g functions, S -square functions and atomic decomposition. Moreover, we further give the characterizations of one-sided Triebel–Lizorkin spaces and the boundedness for commutators. These results complement the missing components in the one-sided singular integral operator and function space theory studied before.