## Banach Journal of Mathematical Analysis

### Hardy-type space estimates for multilinear commutators of Calderón–Zygmund operators on nonhomogeneous 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 a Calderón–Zygmund operator and let $\vec{b}:=(b_{1},\ldots,b_{m})$ be a finite family of $\operatorname{\widetilde{RBMO}}(\mu)$ functions. In this article, the authors establish the boundedness of the multilinear commutator $T_{\vec{b}}$, generated by $T$ and $\vec{b}$ from the atomic Hardy-type space $\widetilde{H}_{\mathrm{fin},\vec{b},m,\rho}^{1,q,m+1}(\mu)$ into the Lebesgue space $L^{1}(\mu)$. The authors also prove that $T_{\vec{b}}$ is bounded from the atomic Hardy-type space $\widetilde{H}_{\mathrm{fin},\vec{b},m,\rho}^{1,q,m+2}(\mu)$ into the atomic Hardy space $\widetilde{H}^{1}(\mu)$ via the molecular characterization of $\widetilde{H}^{1}(\mu)$.

#### Article information

Source
Banach J. Math. Anal., Volume 11, Number 3 (2017), 477-496.

Dates
Accepted: 25 July 2016
First available in Project Euclid: 19 April 2017

https://projecteuclid.org/euclid.bjma/1492618125

Digital Object Identifier
doi:10.1215/17358787-2017-0002

Mathematical Reviews number (MathSciNet)
MR3679892

Zentralblatt MATH identifier
1367.47041

#### Citation

Chen, Jie; Lin, Haibo. Hardy-type space estimates for multilinear commutators of Calderón–Zygmund operators on nonhomogeneous metric measure spaces. Banach J. Math. Anal. 11 (2017), no. 3, 477--496. doi:10.1215/17358787-2017-0002. https://projecteuclid.org/euclid.bjma/1492618125

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