Probability theoretic generalizations of Hardy's and Copson's inequality

被引：2

作者：

Klaassen, Chris A. J. ^{[1
]}

机构：

[1] Univ Amsterdam, Kortewegde Vries Inst Math, Amsterdam, Netherlands

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2023年 / 34卷 / 02期

关键词：

p-norm; Stretched distribution function; Rearrangement lemma;

D O I：

10.1016/j.indag.2022.11.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A short proof of the classic Hardy inequality is presented for p-norms with p > 1. Along the lines of this proof a sharpened version is proved of a recent generalization of Hardy's inequality in the terminology of probability theory. A probability theoretic version of Copson's inequality is discussed as well. Also for 0 < p < 1 probability theoretic generalizations of the Hardy and the Copson inequality are proved. (c) 2022 The Author(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页码：306 / 316

页数：11

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