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A revisit on the compactness of commutators

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  20 August 2020

Weichao Guo ,
Huoxiong Wu  and
Dongyong Yang
Weichao Guo*
Affiliation:
School of Science, Jimei University, Xiamen, 361021, P.R.China
Huoxiong Wu
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P.R. China e-mail: [email protected]@xmu.edu.cn
Dongyong Yang
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P.R. China e-mail: [email protected]@xmu.edu.cn
*
e-mail: [email protected]
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Abstract

A new characterization of $\text {CMO}(\mathbb R^n)$ is established replying upon local mean oscillations. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order commutators.

Keywords

Compactnesscommutatorsingular integralfractional integralCMO ℝn

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 6 , December 2021 , pp. 1667 - 1697
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

Supported by the NSF of China (Nos.11771358, 11871101, 11701112, 11671414, 11971402, and 11871254).

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