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

Abstract

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 $H_{{\rm{at}}}^{1,\;\infty }\left( \mu \right)$ into L ¹ (μ), respectively. As a consequence of these results, they establish the L ^p (μ) boundedness of the commutators on the non-homogeneous metric spaces.

Keywords

Non-homogeneous space / θ-Type Calderón-Zygmund operator / Commutator / RBMO(μ) space / $H_{{\rm{at}}}^{1,\;\infty }\left( \mu \right)$ space