高校应用数学学报B辑
高校應用數學學報B輯
고교응용수학학보B집
APPLIED MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES
2005年
1期
1-9
,共9页
singular integral%Hardy-Sobolev space%rough kernel
The authors study the singular integral operatorTΩ,αf(x)=p.v.∫Rnb(|y|)Ω(y′)|y|-n-α f(x-y)dy,defined on all test functions f,where b is a bounded function,α>0,Ω( y′) is an integrable function on the unit sphere Sn-1 satisfying ce rtain cancellation conditions.It is proved that,for n/(n+α)<p<∞,TΩ,α is a bounded operator from the Hardy-Sobolev space Hpα to t he Hardy space Hp.The results and its applications improve some theorems i n a previous paper of the author and they are extensions of the main theorems in Wheeden's paper(1969).The proof is based on a new atomic decomposition of the s pace Hpα by Han,Paluszynski and Weiss(1995).By using the same p roof,the singluar integral operators with variable kernels are also studied.
