从L^p(R_+~n,ω(x))到L^p(R_+~m)的Hardy型奇异积分算子的(p,p)型范数

On the(p,p) Type Norm of Hardy's Type Singular Integral Operator from L^p(R_+~n,ω(x)) to L^p(R_+~m)

设‖x‖λ=(x1λ+xλ2+…+xλn)1/λ(x∈Rn+),ω(x)是非负可测函数,定义带参数r的从Lp(Rn+,ω(x))到Lp(Rm+)的Hardy型奇异积分算子Tr:Tr(f)(y)=‖y‖1λr∫xλ≤yλf(x)dx,x∈Rn+,y∈Rm+.利用权函数方法,讨论了Tr的(p,p)型范数,并得到其范数的参数表达式.

Suppose ‖x‖λ=（x1^λ＋x2^λ＋…＋xn^λ）^1/λ（x∈Rn^＋）,ω（x）≥0 is a measurable function,Hardy s type singular integral operator Tr with parameter r from L^p（R＋^n,ω（x）toL^p（R＋^m）is defined as Tr（f）（y）=1/‖y‖λ^r∫‖x‖λ≤‖y‖λf（x）dx,x∈Rn^＋,y∈Rm^＋ type norm of operator Tr is obtained by estimating the weight function.