$L^p$ Bounds for the Commutators of Rough Singular Integrals Associated with Surfaces of Revolution

Abstract

In this paper, we establish the $L^p({\Bbb R}^{n+1} )$ boundedness for the commutators of singular integrals associated to surfaces of revolution, $\{(t,\phi(|t|)):t\in {\Bbb R}^{n}\}$, with rough kernels $\Omega\in L(\log L)^2({\Bbb S}^{n-1})$, if $\phi(|t|)=|t|$.