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

• 数学 • 上一篇    下一篇

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

董小莉, 巩万中   

  1. 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   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui 241000, China
  • Received:2018-11-13 Published:2020-01-13

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LMμ,X)为I-凸的当且仅当M ∈ △2(∞)∩ ▽2(∞),且X为I-凸的;LMμ,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: