根据相关的重量函数定义的On Orlicz类
1Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
概括
这项研究探讨了N-函数,使用相关的重量函数和重量序列,对于Orlicz空间至关重要. 结果简化了N函数分析,并将互补的N函数连接到双序列.
科学领域:
- 现实分析 现实分析
- 功能分析是一种功能分析.
- 函数空间函数空间理论
背景情况:
- 对于Orlicz类和空间来说,N函数是基本的.
- 相关的重量函数是超差异化函数类中的关键.
- 重量序列为重量函数提供了基础结构.
研究的目的:
- 用权重序列来描述N函数属性.
- 调查这个框架对抽象N函数的适用性.
- 建立互补N函数和双序列之间的联系.
主要方法:
- 通过相关的重量函数对N函数的分析.
- 使用权重序列对N函数属性的表征.
- 探索抽象的N-功能框架.
主要成果:
- 一些已知的N函数属性纯粹是用权重序列来表达的.
- 这允许构建N函数示例和反示例.
- 在互补的N函数和双序列之间建立了连接.
结论:
- 权重序列框架为研究N函数提供了一个简单而强大的工具.
- 这种方法提高了对Orlicz空间和超差异函数的理解.
- 建立的连接为双序列和互补的N-函数提供了新的见解.
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