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 Hytonen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderon-Zygmund operators with RBMO functions from L∞ (μ) into RBMO(μ) and from $$H_{{\rm{at}}}^{1,\;\infty }\left( \mu \right)$$ 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.