关于N-函数的指标函数的单调性定理

研究生成N-函数的两类数量指标的指标函数的单调性及其关系，主要结果为： (1)设φ为N-函数，φ(t)为它的左导数，记 Fφ(t)=tψ(t) φ(t)，Gφ(c,u)=φ-1(u) φ-1(cu)(c＞1), 则Fφ(t)在(0．φ-1(u0)]单调递增当且仅当对任意c＞1，Gφ(c，u)在(0，u0 c]单调递增． (2)设φ，ψ为一对互余的N-函数，φ，ψ分别为它们的左导数，则(i)Fφ(t)在(0，ψ(C)]上单调递增(递减)当且仅当Fψ(s)在(0，C]上单调递减(递增)；(ii)1／a*φ+1／b*ψ=1．

On the montionial theorems of index function of N-functions

We studied the relationship of the couple of index function of N- ructions, The main results are: (1)Let Fφ(t)= tψ(t) φ(t) Gφ(c,u)=Φ-1(u)Φ-1(cu) (c＞1) where Φ is an N- function and ψ(t) is its left derivative,Then Fφ(t) is increasing on (0, Φ-1 (u0)] iff Gφ(c,u)is increasing on (0,u0c] for all c＞1 (2)Let Φ, ψ be a pair of complementary N-functions,with ψ,ψ are their left derivatives. Then (i) Fφ(t) is increasing (decreasing) on (0,ψ(c)] iff Fψ(s) is decreasing (increasing) on (0,c]. (ii)1a*φ+1b*φ=1,where a*φ=inf{Fφ(t):t∈(0,φ(c)]},b*φ=sup{Fψ(s):s∈(0,c]}.