Abstract view
On the Commutators of Singular Integral Operators with Rough Convolution Kernels


Published:20160418
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
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 $L^q(S^{n1})$ 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
