A Hilbert-type integral inequality in the whole plane related to the hypergeometric function and the beta function

被引：68
作者：
Rassias, Michael Th. [1 ,2 ]
Yang, Bicheng [3 ]
机构：
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[2] ETH, Dept Math, CH-8092 Zurich, Switzerland
[3] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 428卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Hilbert-type integral inequality; Weight function; Equivalent form; Hypergeornetric function; Beta function; OPERATOR; NORM;
D O I：
10.1016/j.jmaa.2015.04.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new Hilbert-type integral inequality in the whole plane with the non-homogeneous kernel and parameters is given. The constant factor related to the hypergeometric function and the beta function is proved to be the best possible. As applications, equivalent forms, the reverses, some particular examples, two kinds of Hardy-type inequalities, and operator expressions are considered. (C) 2015 Published by Elsevier Inc.
引用
收藏
页码：1286 / 1308
页数：23
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