赋p-Amemiya范数的Orlicz函数空间的H_μ性质  

Property H_μ in Orlicz Function Spaces Equipped with the p-Amemiya Norm

作　　者：左明霞[1] 黄悦[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2016年第5期119-124,共6页Journal of Harbin University of Science and Technology

基　　金：黑龙江省教育厅科学技术研究项目(12531137)

摘　　要：讨论了赋p-Amemiya范数‖·‖Φ,p(1<p<")的Orlicz函数空间LΦ中依测度收敛的H性质和Δ2-条件之间的关系.证明了如果Orlicz函数Φ只在零点为零,则赋p-Amemiya范数的Orlicz函数空间LΦ,p具有Hμ性质的充要条件为Φ对所有的实数满足Δ2-条件并且Φ是有限值的;如果Orlicz函数Φ不只在零点为零,则LΦ,p具有Hμ性质的充要条件为Φ在无穷远处满足Δ2-条件并且Φ是有限值的.对于Orlicz函数空间LΦ,p的由序连续的元素所构成的子空间EΦ,p,我们也证明了类似的结论.In this paper, we discuss the relationship between the property H for convergence in measure and the △2-condition for Orlicz function spaces Lφ equipped with the p-Amemiya norm ‖·‖Φ,p（1〈p〈∞）. From our results it follows that if Orlicz Function φ vanishes only at zero, then the Orlicz function spaces equipped with the p-Amemiya norm Lφ,phave property H,, if and only if Orlicz function φ satisfies the △2-condition for all real numbers and φ is finitely valued; if φ vanishes outside zero, then Lφ,p have property Hμ if and only if φ satisfies the △2- condition at infinity and φ is finitely valued. Analogous results are also proved for the subspace Eφ,pof order contin- uous elements of the Orlicz function space Lφ,p.

关 键 词：ORLICZ函数空间 p-Amemiya范数 Hμ性质 Δ2-条件 

分 类 号：O177.3[理学—数学]