AC_k(〔a,b〕,λ).SAC_k(〔a,b〕,λ).WAC_k(〔a,b〕,λ)的若干性质  

Three kinds of absolute continuous functions of order K on the sequence spaces

作　　者：张莉[1] 徐耀群[1] 杨殿军[1] 

机构地区：[1]哈尔滨商业大学基础部,黑龙江哈尔滨150076

出　　处：《哈尔滨工业大学学报》2002年第4期585-586,共2页Journal of Harbin Institute of Technology

基　　金：黑龙江省自然科学基金资助项目 (A0 0 -0 2 )

摘　　要：根据对叙列空间上的K级强绝对连续函数、K级绝对连续函数、K级弱绝对连续函数及x(t)有界且xk(t)为通常的K级绝对连续函数有关性质的讨论 ,得到了与叙列空间上的K级强、弱有界变差函数相似的结论 .证明了在空间S和Φ中 ,上述四种绝对连续是等价的 ,而在 (KB)空间 ,依范K级强、弱绝对连续与K级强、弱绝对连续分别等价 ,从而进一步推广了有关叙列空间上二。Some properties of the Kth order strongly absolute continuous functions,the Kth order absolute continuous functions,the Kth order weakly absolute continuous functions and x(t) is bounded but also x k (t) is the Kth order absolute continuous in general on sequence spaces were investigated,the conclusions are similar as the Kth order strongly and weakly bounded variation functions on the sequence spaces. In the space  S and Φ, the equivalent of four kinds of absolute continuous has been proved,and in (KB)space,the separately equivalent for the Kth order strongly and weakly absolute continuous were obtained. Therefore,the 2th and 3th order absolute continuous functions were extended.

关 键 词：K级强绝对连续函数 K级绝对连续函数 K级弱绝对连续函数 叙列空间 泛涵分析 

分 类 号：O177[理学—数学]