Luxemburg范数下Orlicz-Bochner函数空间的I-凸性与Q-凸性

doi:10.3969/j.issn.1000-5641.201811042

华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (1): 40-50.doi: 10.3969/j.issn.1000-5641.201811042

Luxemburg范数下Orlicz-Bochner函数空间的I-凸性与Q-凸性

董小莉, 巩万中

安徽师范大学数学与统计学院, 安徽芜湖 241000

收稿日期:2018-11-13 发布日期:2020-01-13
通讯作者: 巩万中,男,副教授,研究方向为泛函分析.E-mail:gongwanzhong@shu.edu.cn E-mail:gongwanzhong@shu.edu.cn
基金资助:
国家自然科学基金（11771273）

I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm

DONG Xiaoli, GONG Wanzhong

School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui 241000, China

Received:2018-11-13 Published:2020-01-13

摘要/Abstract

摘要： 根据Banach空间中I-凸与Q-凸的等价定义得到了当（Ω，Σ，μ）为有限测度空间时，Luxemburg范数下Orlicz-Bochner函数空间L_（M）（μ，X）为I-凸的当且仅当M ∈ △₂（∞）∩ ▽₂（∞），且X为I-凸的；L_（M）（μ，X）为Q-凸的当且仅当M ∈ △₂（∞）∩ ▽₂（∞），且X为Q-凸的.

关键词: I-凸性, Q-凸性, Luxemburg范数, Orlicz-Bochner函数空间

Abstract: There are some equivalent definitions for I-convexity and Q-convexity. In this context, if (Ω, Σ, μ) is a finite measure space, the Orlicz-Bochner function space L_(M)(μ, X) endowed with the Luxemburg norm is I-convex if and only if M ∈ △₂(∞) ∩ ▽₂(∞) and X is I-convex; similarly, L_(M)(μ, X) is Q-convex if and only if M ∈ △₂(∞) ∩ ▽₂(∞) and X is Q-convex.

Key words: I-convexity, Q-convexity, Luxemburg norm, Orlicz-Bochner function space

中图分类号:

O177.2

董小莉, 巩万中. Luxemburg范数下Orlicz-Bochner函数空间的I-凸性与Q-凸性[J]. 华东师范大学学报（自然科学版）, 2020, 2020(1): 40-50.

DONG Xiaoli, GONG Wanzhong. I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm[J]. Journal of East China Normal University(Natural Science), 2020, 2020(1): 40-50.

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Luxemburg范数下Orlicz-Bochner函数空间的I-凸性与Q-凸性

I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm

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