Orlicz序列空间的光滑性

Smoothness of Sequence Orlicz Spaces

本文给出Orlics序列空间l光滑性的判据,得出:Orlicz序列空间l光滑的充要条件是,M(u)∈△_2,q(v)在[0,N^(-1)(1/2)]上严格增。其中l表示由N函数M(u)生成的赋Orlicz范数的Orlicz序列空间。q(v)为M(u)的余N函数N(v)的右导数。

The main result of this paper is that the Sequence Orlicz Space generated by N-function M (u) and equipped with Orlicz norm is smooth if and only if M (u) satisfies condition △_2 for small u and q(v) is strictly increasing on [O, N^(-1) (1/2)] where N (V) is the complementary function to M (u) and q (v) its righthand derivative