L^p boundedness of some rough operators with different weights

Abstract

In this paper we prove that the maximal operator M_Ω, the singular integral operator T_Ω, and the maximal singular integral operator T_Ω^* with rough kernels are all bounded operators from L^p(v) to L^p(u) for the weight functions pair (u, v). Here the kernel function Ω satisfies a size condition only; that is, Ω∈ L^q(S^n-1), q>1, but has no smoothness on S^n-1.