Orlicz空间上多项式逼近的逆定理  

The Converse Theorem by Polynomial Approximation in Orlicz Space

作　　者：田园[1] 胡晓敏[1] 张林[1] 

机构地区：[1]杭州电子科技大学理学院数学研究所,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2008年第4期96-98,共3页Journal of Hangzhou Dianzi University：Natural Sciences

摘　　要：该文在Orlicz空间内定义了r-阶的带权连续模以及相应的K-泛函,利用Orlicz空间内带权连续模与K-泛函的等价性以及Orlicz空间上带权的Markov-Bernstein型不等式,从而证明了Or-licz空间上多项式逼近的逆定理。In this paper, an r- th modulus of smoothness with weight and corresponding the k - functional in Orlicz space is introduced. In this paper, using the results of the equivalence theorem between the r-th modulus of smoothness with weight and the k- functional in Orliez space and the weighted Markov - Bemstein type inequality in Orlicz space. We proved the converse polynomial approximation theorem in Orlicz space.

关 键 词：奥尔里奇空间 权函数 马尔可夫-伯恩斯坦型不等式 逆定理 

分 类 号：O174[理学—数学]