The monotonicity of Orlicz-Lorentz spaces equipped with the F-norm

被引：0
|
作者：
Xue, Yangyang [1 ]
Cui, Yunan [1 ]
机构：
[1] Harbin Univ Sci & Technol, Dept Math, Harbin 150080, Peoples R China
来源：
POSITIVITY | 2024年 / 28卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Orlicz-Lorentz spaces; Mazur-Orlicz F-norm; Strict monotonicity; Lower local uniform monotonicity; Upper local uniform monotonicity; GEOMETRIC-PROPERTIES; POINTS;
D O I：
10.1007/s11117-024-01048-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce a new F-normed space, namely Orlicz-Lorentz spaces equipped with the Mazur-Orlicz F-norm. Some basic properties in Orlicz-Lorentz spaces equipped with the Mazur-Orlicz F-norm are given. We find a tool to study the geometry property of Orlicz-Lorentz function spaces, the necessary and sufficient conditions for strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity in Orlicz-Lorentz spaces endowed with the Mazur-Orlicz F-norm are obtained without any assumptions. The tool also can simplify the proof of the corresponding results of Orlicz-Lorentz spaces equipped with the Luxemburg norm without condition (+).
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页数：18
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