A ROUGH HYPERSINGULAR INTEGRAL OPERATOR WITH AN OSCILLATING FACTOR ON FUNCTION SPACE  

作　　者：Ye Xiaofeng Dept.of Math.,Zhejiang Univ.,Hangzhou 310027,China Dept.of Math.,East China JiaoTong Univ.,Nanchang 330013,China. 

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2007年第4期449-452,共4页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National 973 Program of China(1999075105);National Natural Science Foundation of China(10271107);RFDP(20030335019);Natural Science Foundation of Zhejiang Proyince(RC97017)

摘　　要：The singular integral operatorTα,βf（x）=p.v.∫R^n[e^i｜y｜^-βΩ（y’）]/[｜y｜^n＋α]f（x-y）dy,defined for all test functions f is studied, where Ω（y＇） is a distribution on the unit sphere S^n-1 satisfying certain cancellation condition. It is proved that Tα,β is a bounded operator from the Triebel-Lizorkin space Fp^s,q to the Triebel-Lizorkin space Fp^s＋γ,q, provided that Ω（y＇） is a distribution in the Hardy space H^r（S^n-1） with r = （n - 1）/（n - 1 ＋ γ）.The singular integral operatorTα,βf（x）=p.v.∫R^n[e^i｜y｜^-βΩ（y’）]/[｜y｜^n＋α]f（x-y）dy,defined for all test functions f is studied, where Ω（y＇） is a distribution on the unit sphere S^n-1 satisfying certain cancellation condition. It is proved that Tα,β is a bounded operator from the Triebel-Lizorkin space Fp^s,q to the Triebel-Lizorkin space Fp^s＋γ,q, provided that Ω（y＇） is a distribution in the Hardy space H^r（S^n-1） with r = （n - 1）/（n - 1 ＋ γ）.

关 键 词：Hardy space hypersingular integral. 

分 类 号：O174[理学—数学]