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

• Published in: The Journal of geometric analysis Vol. 33; no. 9
• Main Authors: Fu, Zunwei, Hou, Xianming, Lee, Ming-Yi, Li, Ji
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2023; Springer Nature B.V
• Subjects: Abstract Harmonic Analysis; Commutators; Convex and Discrete Geometry; Differential Geometry; Dynamical Systems and Ergodic Theory; Fourier Analysis; Function space; Geometry; Global Analysis and Analysis on Manifolds; Mathematics; Mathematics and Statistics; Operators (mathematics); Primary 42B20; Commutator; 42B35; 42B30; Calderón reproducing formula; One-sided Hardy space; One-sided Triebel–Lizorkin space; Secondary 42B25; Atomic decomposition

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 resul...