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

Citation:

Chol RI,Zhenqiu ZHANG.Boundedness of Commutators of θ-Type Calderόn-Zygmund Operators on Non-homogeneous Metric Measure Spaces[J].Chinese Annals of Mathematics B,2019,40(4):585~598
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Authors:

Chol RI; Zhenqiu ZHANG

Foundation:

This work was supported by the National Natural Science Foundation of China (No.11671414).
Abstract: Let $(X,d,\mu)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt\"{o}nen. In this paper, the authors obtain the boundedness of the commutators of $\theta$-type Calder\'{o}n-Zygmund operators with ${\rm RBMO}$ functions from $L^{\infty}(\mu)$ into ${\rm RBMO}(\mu)$ and from $H^{1,\infty}_{\rm at}(\mu)$ into $L^{1}(\mu),$ respectively. As a consequence of these results, they establish the $L^{p}(\mu)$ boundedness of the commutators on the non-homogeneous metric spaces.

Keywords:

Non-homogeneous space, $,theta,$-Type Calder'{o}n-Zygmundoperator, Commutator, ${rm RBMO}(mu)$ space, $H^{1,infty}_{rmat}(mu)$ space

Classification:

42B20
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