Commutators of Riesz transforms

Gong Ru-Ming

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Commutators of Riesz transforms

Gong Ru-Ming

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006

*Correspondence author

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Funding: Specialized Research Fund for the Doctoral Program of Higher Education （No.Grant No. 20124410120002）

Opened online:15 December 2015

Accepted by: none

Citation: Gong Ru-Ming.Commutators of Riesz transforms[OL]. [15 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4669969

Let $A$ be a Laplacian operator associated with a quadratic formon $Omega$ where $Omega$ is the Euclidean space $mathbb{R}^n$ ora domain of $mathbb{R}^n$. In this paper, we show that when afunction $bin BMO(Omega)$, the commutators $[b,igtriangledownA^{-1/2}]$ are bounded on $L^p(Omega)$ for all $1<p<2$, where theoperators $igtriangledown A^{-1/2}$ are Riesz transformsassociated with $A$.

Keywords:Riesz transform, commutators, BMO.

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