赋广义Orlicz范数的Orlicz函数空间的一致凸性

J4 ›› 2011, Vol. 49 ›› Issue (05): 809-813.

赋广义Orlicz范数的Orlicz函数空间的一致凸性

段丽芬¹, 许晶^1,2, 崔云安²

1. 通化师范学院数学系, 吉林通化 134002； 2. 哈尔滨理工大学应用科学学院, 哈尔滨 150080

收稿日期:2010-11-29 出版日期:2011-09-26 发布日期:2011-09-27
通讯作者: DUAN Lifen E-mail:duanlf@126.com

Uniform Rotundity in Orlicz Function Spaces Equipped with Generalized Orlicz Norm

DUAN Lifen¹, XU Jing^1,2, CUI Yunan²

1. Department of Mathematics, Tonghua Normal University, Tonghua 134002, Jilin Province, China;2. College of Applied Sciences, Harbin University of Science and Technology, Harbin 150080, China

Received:2010-11-29 Online:2011-09-26 Published:2011-09-27
Contact: 段丽芬 E-mail:duanlf@126.com

摘要/Abstract

摘要：

利用Banach及经典Orlicz空间几何理论, 研究赋广义Orlicz范数的Orlicz函数空间一致凸问题, 得到了由右导函数为凸函数的N函数生成的赋广义Orlicz范数的Orlicz函数空间一致凸的充要条件.

关键词: 广义Orlicz范数； Orlicz函数空间；一致凸

Abstract:

By means of geometries of Banach spaces and Orlicz spaces method, the characterizations over uniform rotundity of the Orlicz function spaces equipped with the generalized Orlicz norm was discussed. For the Orlicz function spaces generated by a Nfunction whose derivative on the right is convex and equipped with the generalized Orlicz norm, both sufficient and necessary conditions were presented to make them be uniform rotund.

Key words: generalized Orlicz norm, Orlicz function space, uniform rotund

中图分类号:

O177.3

段丽芬, 许晶, 崔云安. 赋广义Orlicz范数的Orlicz函数空间的一致凸性[J]. J4, 2011, 49(05): 809-813.

DUAN Li-Fen, HU Jing, CUI Yun-An. Uniform Rotundity in Orlicz Function Spaces Equipped with Generalized Orlicz Norm[J]. J4, 2011, 49(05): 809-813.