空间(L_μ~p)~m的弱Banach-Saks性质(英文)  

Weak Banach-Saks Property of Space(L_μ~p)~m

作　　者：姜正禄[1] 傅小勇[1] 

机构地区：[1]中山大学数学系,广州510275

出　　处：《应用泛函分析学报》2009年第3期193-200,共8页Acta Analysis Functionalis Applicata

基　　金：NSFC(10271121);the Scientific Reseach Foundation for the Returned Overseas Chinese Scholars,the Education Ministry of China and joint grants of NSFC(10511120278,10611120371);RFBR(04-02-39026)

摘　　要：证明了由m个Lμp空间产生的Banach向量空间(Lμp)m的弱Banach-Saks性质,其中m是自然数, 1 p <+∞.当m= 1时,这就是著名的Banach-Saks-Szlenk定理.运用该性质,还给出了定义在向量空间Rm的一个凸集上的非负连续凸函数与取值在空间(Lpμ)m的一个弱紧子集中的向量值函数的复合函数的积分不等式.当这些向量值函数属于由m个Lμ∞空间产生的积空间(Lμ∞)m的一个弱*紧子集时,类似的积分不等式还是成立的.We show the weak Banach-Saks property of the Banach vector space（Lpμ）m generated by m Lpμ-spaces for 1≤p〈＋∞,where m is any given natural number.When m=1,this is the famous Banach-Saks-Szlenk theorem.By use of this property,we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of a vector space Rm and vector-valued functions in a weakly compact subset of the space（Lpμ）m for 1≤〈＋∞ and inequalities when these vector-valued functions are in a weakly^＊ compact subset of the product space （Lμ^p）^m generated by m Lμ^p -spaces.

关 键 词：凸函数 可测空间 LEBESGUE积分 BANACH空间 

分 类 号：O177.2[理学—数学]