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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 commutator, singular integral operator, compact operator, completely continuous operator, maximal operator, Morrey space
MSC Classifications: 42B20, 47B07 show english descriptions Singular and oscillatory integrals (Calderon-Zygmund, etc.)
Operators defined by compactness properties
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
47B07 - Operators defined by compactness properties
 

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