Rough singular integrals associated with surfaces of Van der Corput type

摘要

In this paper,the authors establish the Lp-mapping properties for a class of singular integrals along surfaces in Rn of the form {φ(|u|)u : u ∈ Rn} as well as the related maximal operators provided that the function φ satisfies certain oscillatory integral estimates of Van der Corput type,and the integral kernels are given by the radial function h ∈Δγ(R+) for γ > 1 and the sphere function Ω∈ Fβ(Sn.1) for some β > 0,which is distinct from H1(Sn.1).