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

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.