华东师范大学学报（自然科学版） >

2020 , Vol. 2020 >Issue 1: 40 - 50

DOI: https://doi.org/10.3969/j.issn.1000-5641.201811042

数学

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

  • 董小莉 ,
  • 巩万中
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  • 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

  网络出版日期: 2020-01-13

基金资助

国家自然科学基金（11771273）

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

  • DONG Xiaoli ,
  • GONG Wanzhong
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  • School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui 241000, China

Received date: 2018-11-13

  Online published: 2020-01-13

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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

本文引用格式

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 . DOI: 10.3969/j.issn.1000-5641.201811042

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

参考文献

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