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The commutators of multilinear Calderón–Zygmund operators on weighted Hardy spaces

Part of: Special classes of linear operators Harmonic analysis in several variables

Published online by Cambridge University Press:  26 June 2023

Yanyan Han ,
Yongming Wen ,
Huoxiong Wu  and
Qingying Xue
Yanyan Han
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, People's Republic of China ([email protected]) School of Information Network Security, People's Public Security University of China, Beijing 100038, People's Republic of China
Yongming Wen
Affiliation:
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, People's Republic of China ([email protected])
Huoxiong Wu
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, People's Republic of China ([email protected])
Qingying Xue
Affiliation:
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing 100875, People's Republic of China ([email protected])
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Abstract

In this paper, we study the behaviours of the commutators $[\vec b,\,T]$ generated by multilinear Calderón–Zygmund operators $T$ with $\vec b=(b_1,\,\ldots,\,b_m)\in L_{\rm loc}(\mathbb {R}^n)$ on weighted Hardy spaces. We show that for some $p_i\in (0,\,1]$ with $1/p=1/p_1+\cdots +1/p_m$, $\omega \in A_\infty$ and $b_i\in \mathcal {BMO}_{\omega,p_i}$ ($1\le i\le m$), which are a class of non-trivial subspaces of ${\rm BMO}$, the commutators $[\vec b,\,T]$ are bounded from $H^{p_1}(\omega )\times \cdots \times H^{p_m}(\omega )$ to $L^p(\omega )$. Meanwhile, we also establish the corresponding results for a class of maximal truncated multilinear commutators $T_{\vec b}^*$.

Keywords

BMO spacescommutatorsmultilinear Calderón–Zygmund operatorsweighted Hardy spaces

MSC classification

Primary: 47B47: Commutators, derivations, elementary operators, etc.
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B30: $H^p$-spaces 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 4 , August 2024 , pp. 1259 - 1280
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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