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

董小莉; 巩万中

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

doi: 10.3969/j.issn.1000-5641.201811042

董小莉,
巩万中^,

安徽师范大学数学与统计学院, 安徽芜湖　241000

基金项目: 国家自然科学基金(11771273)

详细信息

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

中图分类号: O177.2
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- 文章访问数: 83
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- 被引次数: 0
出版历程
- 收稿日期: 2018-11-13
- 网络出版日期: 2019-12-25
- 刊出日期: 2020-01-01

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

摘要

摘要: 根据Banach空间中I-凸与Q-凸的等价定义得到了当$(\Omega,\Sigma,\mu)$为有限测度空间时, Luxemburg范数下Orlicz-Bochner函数空间$L_{(M)}(\mu, X)$为I-凸的当且仅当$M\in{\Delta}_2(\infty)\cap$$ {\nabla}_2(\infty)$, 且$X$为I-凸的; $L_{(M)}(\mu,X)$为Q-凸的当且仅当$M\in{\Delta}_2(\infty)\cap{\nabla}_2(\infty)$, 且$X$为Q-凸的.
- 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 $(\Omega,\Sigma,\mu)$ is a finite measure space, the Orlicz-Bochner function space $L_{(M)}(\mu,X)$ endowed with the Luxemburg norm is I-convex if and only if $M\in{\Delta}_2(\infty)\cap{\nabla}_2(\infty)$ and $X$ is I-convex; similarly, $L_{(M)}(\mu,X)$ is Q-convex if and only if $M\in{\Delta}_2(\infty)\cap{\nabla}_2(\infty)$ and $X$ is Q-convex.
- I-convexity /
- Q-convexity /
- Luxemburg norm /
- Orlicz-Bochner function space

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参考文献(16)

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