[1]黄 红,袁俊丽.含有有限项的Hardy-Littlewood-Plya不等式[J].南京师大学报(自然科学版),2023,46(03):26-30.[doi:10.3969/j.issn.1001-4616.2023.03.005]
　Huang Hong,Yuan Junli.Hardy-Littlewood-Plya Inequality Containing Finite Terms[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(03):26-30.[doi:10.3969/j.issn.1001-4616.2023.03.005]
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含有有限项的Hardy-Littlewood-Pólya不等式()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第46卷
期数:
2023年03期
页码:
26-30
栏目:
数学
出版日期:
2023-09-15

文章信息/Info

Title:
Hardy-Littlewood-Pólya Inequality Containing Finite Terms
文章编号:
1001-4616(2023)03-0026-05
作者:
黄 红1; 袁俊丽2
(1.南京师范大学中北学院,江苏 镇江 212334)
(2.无锡学院理学院,江苏 无锡 214000)
Author(s):
Huang Hong1; Yuan Junli2
(1.Zhongbei College,Nanjing Normal University,Zhenjiang 212334,China)
(2.College of Science,Wuxi University,Wuxi 214000,China)
关键词:
Hardy-Littlewood-Pó; lya不等式; 上下界估计; 最佳常数
Keywords:
Hardy-Littlewood-Pó; lya inequality;  estimates of the upper and the lower bounds;  best constant
分类号:
O178
DOI:
10.3969/j.issn.1001-4616.2023.03.005
文献标志码:
A
摘要:
本文证明了含有有限项的Hardy-Littlewood-Pólya不等式,并借助其极值函数满足的Euler-Lagrange方程组,估计这个不等式最佳常数的上下界.
Abstract:
We prove Hardy-Littlewood-Pólya inequality containing finite terms. The authors also give the estimates of the upper and the lower bounds of the best constant with the help of the Euler-Lagrange equations,which is satisfied by extreme functions of Hardy-Littlewood-Pólya inequality.

参考文献/References:

[1]HARDY G H,LITTLEWOOD J E,PLYA G. Inequalities[M]. Cambridge:Cambridge University Press,1952.
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[7]LI C M,VILLAVERT J. An extension of the Hardy-Littlewood-Pólya inequality[J]. Acta mathematica scientia,2011,31(B):2285-2288.
[8]CHENG Z,LI C M. An extended discrete Hardy-Littlewood-Sobolev inequality[J]. Discrete and continuous dynamical systems,2014,34:1951-1959.
[9]LIEB E H. Coberent states as a tool for obtaining rigorous bounds[C]//Proceedings of the Symposium on Coberent States,past,present and future. Oak Ridge:World Scientific,1994:267-278.
[10]HUANG G G,LI C M,YIN X M. Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality[J]. Discrete and continuous dynamical systems,2015,35:935-942.

备注/Memo

备注/Memo:
收稿日期:2023-04-24.
基金项目:国家自然科学基金项目(11871278)、无锡学院人才启动项目(550221025).
通讯作者:袁俊丽,博士,副教授,研究方向:偏微分方程及应用. E-mail:860166@cwxu.edu.cn
更新日期/Last Update: 2023-09-15