二级绝对连续函数空间(Ⅰ)

<正> 闵嗣鹤、董怀允、郭大钧等结合广义调和分析论,定义了二级囿变函数和二级Stieltjes积分,并对其性质做了一系列研究(参看[1]—[3])。李子平在[4]中引进了二级绝对连续函数的概念,证明了它的一个充分必要条件,从而将二级Stieltjes积分的计算化成了Lebesgue积分的计算。之后,李文清、吴从炘等将囿变函数和二级囿变函数的概念推广到序

ON FHE SPACES OF ABSOLUTELY CON TINUOUS FUNCTIONS OF ORDER 2(Ⅰ)

Jhe main prupose of this paper i's to discuss SOme properties of the spaces of absolatelg continuoas fanctions of order 2 Which defined on the Closed interu al [a,b].We havefirst induced the norm in real(AC_2[a,b],and proved that ti is a real Banach algera. ln section two we generate fhe notion of real absolutelg Continuous functions of or der 2 to the complex case, and show that complex Ac_2 [a, b] is a normed ring.In section Three we have discussed some properties of tlis normed ring and show that Complex AC_2 [a, b] is semi-sinple, points separated and regular.