Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 875649, 15 pages
doi:10.1155/2011/875649
Research Article

Nonsquareness and Locally Uniform Nonsquareness in Orlicz-Bochner Function Spaces Endowed with Luxemburg Norm

Shaoqiang Shang,1 Yunan Cui,2 and Yongqiang Fu1

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Received 5 July 2010; Accepted 12 February 2011

Academic Editor: Nikolaos Papageorgiou

Copyright © 2011 Shaoqiang Shang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Criteria for nonsquareness and locally uniform nonsquareness of Orlicz-Bochner function spaces equipped with Luxemburg norm are given. We also prove that, in Orlicz-Bochner function spaces generated by locally uniform nonsquare Banach space, nonsquareness and locally uniform nonsquareness are equivalent.