Boundedness of Commutators of θ-Type Calderón-Zygmund Operators on Non-homogeneous Metric Measure Spaces

Let (X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hytönen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderón-Zygmund operators with RBMO functions from L∞ (μ) into RBMO(μ) and from Hat1,∞(μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{{\rm{at}}}^{1,\;\infty }\left( \mu \right)$$\end{document} into L1 (μ), respectively. As a consequence of these results, they establish the Lp (μ) boundedness of the commutators on the non-homogeneous metric spaces.