Rough singular integrals associated with surfaces of Van der Corput type  

作　　者：LIU Feng WU Huo-xiong 

机构地区：[1]School of Mathematical Sciences,Xiamen University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2014年第1期86-100,共15页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11071200,11371295)

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）.

关 键 词：42B20 42B25 42B30 Singular integrals surfaces of Van der Corput type maximal operators Littlewood-Paley theory  Fourier transform estimates 

分 类 号：O172.2[理学—数学] P618.130.2[理学—基础数学]