Taiwanese Journal of Mathematics

VECTOR VALUED COMMUTATORS ON NON-HOMOGENEOUS SPACES

Wengu Chen and Changxing Miao

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Abstract

Let $\mu$ be a Borel measure on $\mathbb{R}^d$ which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(Q) \leq c_0 l(Q)^n$ for any cube $Q \subset \mathbb{R}^d$ with sides parallel to the coordinate axes and for some fixed $n$ with $0 \lt n \leq d$. This paper is to develop the vector valued commutator theory in the context of the non-thomogeneous spaces. As an application, the boundedness of the maximal commutator of any Calderón-Zygmund operator on the non-homogeneous space with a $RBMO(\mu)$ function introduced by Tolsa in [9] is obtained.

Article information

Source
Taiwanese J. Math., Volume 11, Number 4 (2007), 1127-1141.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404808

Digital Object Identifier
doi:10.11650/twjm/1500404808

Mathematical Reviews number (MathSciNet)
MR2348557

Zentralblatt MATH identifier
1213.42036

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Keywords
Calderón-Zygmund operator commutator non-doubling measure

Citation

Chen, Wengu; Miao, Changxing. VECTOR VALUED COMMUTATORS ON NON-HOMOGENEOUS SPACES. Taiwanese J. Math. 11 (2007), no. 4, 1127--1141. doi:10.11650/twjm/1500404808. https://projecteuclid.org/euclid.twjm/1500404808


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