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

【Author】

Chol RI;Zhenqiu ZHANG;Department of Mathematics, Kim Hyong Jik Normal University;School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics,Nankai University;

【Institution】

Department of Mathematics, Kim Hyong Jik Normal University;School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics,Nankai University;

【Abstract】

Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. 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_(at)~(1,∞)(μ) 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_(at)~(1,∞)(μ) space

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