On certain rough maximal operators and singular integrals

Abstract

We study the L p mapping properties of a class of singular integral operators T p,Ω,h related to polynomial mappings. We prove that this class of singular operators and some of its related maximal operators are bounded on L p when the kernel function Ω in L(log L) α(S n-1) for some α > 0 and theradial function h(|x|) satisfies a mild integrability condition.