## Taiwanese Journal of Mathematics

### Maximal Multilinear Commutators on Non-homogeneous Metric Measure Spaces

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 21, Number 5 (2017), 1133-1160.

Dates
Revised: 21 January 2017
Accepted: 24 January 2017
First available in Project Euclid: 1 August 2017

https://projecteuclid.org/euclid.twjm/1501599186

Digital Object Identifier
doi:10.11650/tjm/7976

Mathematical Reviews number (MathSciNet)
MR3707887

Zentralblatt MATH identifier
06871362

#### Citation

Chen, Jie; Lin, Haibo. Maximal Multilinear Commutators on Non-homogeneous Metric Measure Spaces. Taiwanese J. Math. 21 (2017), no. 5, 1133--1160. doi:10.11650/tjm/7976. https://projecteuclid.org/euclid.twjm/1501599186

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