可积函数HÖlder不等式的等价不等式
Equivalent Inequalities of the HÖlder Inequality for Integrable Functions
DOI: 10.12677/AAM.2023.123108, PDF, HTML, 下载: 137  浏览: 248  科研立项经费支持
作者: 沈诗雨, 张盛婕, 张文彬：常熟理工学院，数学与统计学院，江苏 常熟
关键词: HÖlder不等式；算术平均-几何平均不等式；喜平均不等式；等价性；HÖlder Inequality； AM-GM Inequality； Power Average Inequality； Equivalence
摘要: HÖlder不等式在分析学和初等不等式理论中扮演着极其重要的角色。作为相关研究的一个重要方面, 它与其它不等式之间的等价关系的研究也越来越受到重视。本文证明了测度空间上积分形式的H¨older不等式与算术平均-几何平均不等式,以及它与喜平均不等式之间的等价关系。这些结果极大地推广了李勇涛等最近建立的离散不等式等价关系。
Abstract: HÖlder inequality plays an extremely important role in analysis and elementary in- equality theory. As an important aspect of related research, the study of its equiva-lence relationship with other inequalities has also received increasing attention. This paper proves the H¨older inequality and the AM-GM inequality in measure space, and its equivalence relationship with the power mean inequality. These results generalize the discrete inequality equivalence relationship recently established by Li etal.
文章引用：沈诗雨, 张盛婕, 张文彬. 可积函数HÖlder不等式的等价不等式[J]. 应用数学进展, 2023, 12(3): 1068-1076. https://doi.org/10.12677/AAM.2023.123108

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