论文摘要
Orlicz-Lorentz空间中定性的几何性质,已被很多学者关注,由于重排所产生的困难,与经典Orlicz空间中并列的定量几何性质（几何常数）却没有什么研究成果.所以,研究Orlicz-Lorentz序列空间中的Riesz角就很有意义了,它可以为定量性质的研究提供一种框架.本文在Orlicz-Lorentz序列空间中分别对赋Luxemburg范数与Orlicz范数的Riesz角进行了研究,即利用各种数量指标来估计Riesz角的上界和下界,它们在指标函数满足某种单调性的条件下可以重合,从而使Riesz角取得精确值.本文的主要结果是Riesz角α（λΦ，ω）与α（λΦ，ωo）满足这个结果推广了任重道的有关工作.作为推论,我们得到：（1）Lorentz空间λp，ω的Riesz角为21/p;（2）α（λΦ，ω）<2当且仅当Φ∈▽2（0）,当且仅当α（λΦ，ωo）<2.全文共分为三个章节,主要工作总结如下：第一章是预备知识,主要给出本文涉及的一些基本概念,记号以及一些基础引理.第二章给出了赋Luxemburg范数的Orlicz-Lorentz序列空间中的Riesz角的上界与下界,计算出了由某些特殊的N-函数与权序列定义的空间中Riesz角的合理范围.在第三章,我们转向赋Orlicz范数的Orlicz-Lorentz序列空间中的Riesz角的估计,通过注记和推论,所给的表达式都是实际可操作的.
论文目录
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