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Boundedness of Commutators of θ-Type Calderόn-Zygmund Operators on Non-homogeneous Metric Measure Spaces |
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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 |
Page view: 1421
Net amount: 1127 |
Authors: |
Chol RI; Zhenqiu ZHANG |
Foundation: |
This work was supported by
the National Natural Science Foundation of China (No.11671414). |
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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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