摘要
In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф(lul)u' : u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ(R+) for γ 〉 1 and the sphere function ΩεFβ(S^n-1) for someβ 〉 0 which is distinct from HI(Sn-1).
In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф(lul)u' : u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ(R+) for γ 〉 1 and the sphere function ΩεFβ(S^n-1) for someβ 〉 0 which is distinct from HI(Sn-1).
基金
Supported by the National Natural Science Foundation of China(11071200,11371295)