摘要
对于n元连续周期函数及其共轭函数,由Γ_R(f)(x)=∫_(|y|>1)f(x-y/R)|y|^(-n-1)dy(R>0)定义的算子Γ_R在全测度集上的逼近性态被讨论且所得的结果被用来得到对于用S_R(f)(x)=sum from|m|<R to ((1-m/r)^((n-1)/2) a_m(f)e^(imx))定义的广义Riesz平均的逼近的估计。
For continuaus periodic functions of n variables (n≥2)and their conjugate functions the approximation behaviour on set of full measure of the operators Γ_R defined by Γ_R(f)(x)=∫_(|y|>1)f(x-y/R)|y|^(-n-1)dy(R>0)is discussed and the result is applied to get the estimate for approximation by generalized Riesz means S_R defined as S_R(f)(x)=sum from|m|<R to ((1-m/r)^((n-1)/2) a_m(f)e^(imx)).
出处
《北京师范大学学报（自然科学版）》
CAS
1987年第4期1-8,共8页
Journal of Beijing Normal University(Natural Science)
基金
国家科学基金
