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October, 2017 Maximal Multilinear Commutators on Non-homogeneous Metric Measure Spaces
Jie Chen, Haibo Lin
Taiwanese J. Math. 21(5): 1133-1160 (October, 2017). DOI: 10.11650/tjm/7976

Abstract

Let $(\mathcal{X},d,\mu)$ be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let $T_*$ be the maximal Calderón-Zygmund operator and $\vec{b} := (b_1,\ldots,b_m)$ be a finite family of $\widetilde{\operatorname{RBMO}}(\mu)$ functions. In this paper, the authors establish the boundedness of the maximal multilinear commutator $T_{*,\vec{b}}$ generated by $T_*$ and $\vec{b}$ on the Lebesgue space $L^p(\mu)$ with $p \in (1, \infty)$. For $\vec{b} = (b_1,\ldots,b_m)$ being a finite family of Orlicz type functions, the weak type endpoint estimate for the maximal multilinear commutator $T_{*,\vec{b}}$ generated by $T_*$ and $\vec{b}$ is also presented. The main tool to deal with these estimates is the smoothing technique.

Citation

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Jie Chen. Haibo Lin. "Maximal Multilinear Commutators on Non-homogeneous Metric Measure Spaces." Taiwanese J. Math. 21 (5) 1133 - 1160, October, 2017. https://doi.org/10.11650/tjm/7976

Information

Received: 27 June 2016; Revised: 21 January 2017; Accepted: 24 January 2017; Published: October, 2017
First available in Project Euclid: 1 August 2017

zbMATH: 06871362
MathSciNet: MR3707887
Digital Object Identifier: 10.11650/tjm/7976

Subjects:
Primary: 47B47
Secondary: 30L99, 42B20, 42B35

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 5 • October, 2017
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