Lp boundedness of some rough operators with different weights

Source abstract

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