赋Orlicz范数的模函数空间的单调性  

Monotonicity in Modular Function Spaces Equipped with O-norm

作　　者：胡雪梅 崔云安 HU Xuemei;CUI Yunan(School of Electric and Engineering,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2024年第2期153-158,共6页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181).

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。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 

分 类 号：O177.2[理学—数学]