$L\sp 2({\Bbb R}\sp n)$ boundedness for the commutators of convolution operators

Abstract

The commutators of convolution operators are considered. By localization and Fourier transform estimates, a sufficient condition such that these commutators are bounded on $L^2(\mathbb{R}^n)$ is given. As applications, some new results about the $L^2(\mathbb{R}^n)$ boundedness for the commutators of homogeneous singular integral operators are established.