赋Orlicz范数的模函数空间的单调性
Monotonicity in Modular Function Spaces Equipped with O-norm
胡雪梅 1崔云安1
作者信息
- 1. 哈尔滨理工大学 理学院,哈尔滨 150080
- 折叠
摘要
模空间是经典Lebesgue和Orlicz空间的推广.在模空间引入Orlicz范数,研究赋Luxemburg范数模空间与赋Orlicz范数模空间的单调性.首先证明了模空间中Luxemburg范数与Orlicz范数是等价的,且赋Orlicz范数模空间是Banach空间,其次证明了赋Orlicz范数模空间是严格单调的,最后给出了赋Luxemburg范数模空间是严格单调的充要条件.
Abstract
Modular function spaces are extensions of Lebesgue spaces and Orlicz spaces.We introduce Orlicz norm in Modular function spaces,and study the monotonicity in modular function spaces equipped with O-norm and L-norm.Firstly,the paper demonstrates O-norm is equivalent to L-norm in modular function spaces,and modular function spaces equipped with O-norm are Banach spaces.Then,the paper demonstrates modular function spaces equipped with O-norm are strictly monotone.Lastly,the necessary and sufficient conditions of strict monotonicity of modular function spaces equipped with L-norm are given.
关键词
模函数空间/Orlicz范数/严格单调性/Luxemburg范数Key words
modular function space/O-norm/strict monotonicity/L-norm引用本文复制引用
出版年
2024
NETL
NSTL
万方数据