Algebras of Calderón–Zygmund Operators on Spaces of Homogeneous Type

In this paper, using continuous Calderón’s reproducing formulas, we obtain algebras of Calderón–Zygmund operators on spaces of homogenous type in the setting of both one parameter and bi-parameter. More precisely, all classical Calderón–Zygmund operators form an algebra when T(1)=T∗(1)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T(1)=T^*(1)=0$$\end{document} and all product singular integral operators in Journé’s class form an algebra when T1(1)=T1∗(1)=T2(1)=T2∗(1)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1(1)=T_1^*(1)=T_2(1)=T_2^*(1)\,{=}\,0$$\end{document}.