摘要
A.Dol和B.Eckman在〔1〕中讨论了广义Orlicz空间上的连续线性泛函,但是他对函数Φ(t,u)的要求是苛刻的。这就使得〔1〕所讨论的问题仍然没有超出N-函数的范围。本文将条件1°去掉,在此情况下得出,对任意y∈L~φ,f(x)=∫x(t)y(t)dμ(x∈L~φ)是L~φ上的模连续性泛函,从而改进了〔1〕的结果。
Abstrat A. Dold and B. Eckman discussed continuous linear fuctional in genaralived Orliz space Lφ and it wos suppoosed that the φ-fuction φ(t,u) satisfies the following conditions,1°φ(t,u) is a generalized N-function: 2°φ(t,u) is locally integrabl;3°for each n0<0,there exists a>0 such that φ(t,u)/u>a for u>u0 In this paper we remove the fist condition and prove the following theorem.
Let φCbe loally integrable and there exists a U>0 such that u<(t,u) for u>u0.Then for each y L, f(x) = (t)y(t)du (x L) is a coutinuou linear functional in L.
出处
《黑龙江大学自然科学学报》
CAS
1989年第3期14-17,共4页
Journal of Natural Science of Heilongjiang University
关键词
广义ψ函数
ORLICZ空间
模收敛
modular, modular convergence, generalized gb-ftillction, generalizedOrlicz space.
