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# On the Commutators of Singular Integral Operators with Rough Convolution Kernels

Published:2016-04-18
Printed: Aug 2016
• Xiaoli Guo,
Department of Mathematics and Information Science, Zhengzhou University of Light Industry,, Zhengzhou 450002, P. R. China
• Guoen Hu,
Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450001, P. R. China
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## Abstract

Let $T_{\Omega}$ be the singular integral operator with kernel $\frac{\Omega(x)}{|x|^n}$, where $\Omega$ is homogeneous of degree zero, has mean value zero and belongs to $L^q(S^{n-1})$ for some $q\in (1,\,\infty]$. In this paper, the authors establish the compactness on weighted $L^p$ spaces, and the Morrey spaces, for the commutator generated by $\operatorname{CMO}(\mathbb{R}^n)$ function and $T_{\Omega}$. The associated maximal operator and the discrete maximal operator are also considered.
 Keywords: commutator, singular integral operator, compact operator, completely continuous operator, maximal operator, Morrey space
 MSC Classifications: 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 47B07 - Operators defined by compactness properties

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