可积函数HÖlder不等式的等价不等式  

Equivalent Inequalities of the HÖlder Inequality for Integrable Functions

作　　者：沈诗雨 张盛婕 张文彬 

机构地区：[1]常熟理工学院,数学与统计学院,江苏 常熟

出　　处：《应用数学进展》2023年第3期1068-1076,共9页Advances in Applied Mathematics

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。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.

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 

分 类 号：O17[理学—数学]