Banach Journal of Mathematical Analysis

Hardy-type space estimates for multilinear commutators of Calderón–Zygmund operators on nonhomogeneous metric measure spaces

Jie Chen and Haibo Lin

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Abstract

Let (X,d,μ) 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 b:=(b1,,bm) be a finite family of \widetilde{RBMO}(μ) functions. In this article, the authors establish the boundedness of the multilinear commutator Tb, generated by T and b from the atomic Hardy-type space H˜fin,b,m,ρ1,q,m+1(μ) into the Lebesgue space L1(μ). The authors also prove that Tb is bounded from the atomic Hardy-type space H˜fin,b,m,ρ1,q,m+2(μ) into the atomic Hardy space H˜1(μ) via the molecular characterization of H˜1(μ).

Article information

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

Dates
Received: 28 April 2016
Accepted: 25 July 2016
First available in Project Euclid: 19 April 2017

Permanent link to this document
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

Subjects
Primary: 47B47: Commutators, derivations, elementary operators, etc.
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35: Function spaces arising in harmonic analysis 30L99: None of the above, but in this section

Keywords
nonhomogeneous metric measure space multilinear commutator Calderón–Zygmund operator $\widetilde{\mathrm{RBMO}}(\mu)$ space Hardy-type space

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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