On a composition of two Hilbert-Hardy-type integral operators and related inequalities

被引：1

作者：

Yang, Bicheng ^{[1
]}

Chen, Qiang ^{[2
]}

机构：

[1] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China

[2] Guangdong Univ Educ, Dept Comp Sci, Guangzhou 510303, Guangdong, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2015年

基金：

中国国家自然科学基金;

关键词：

Hilbert-Hardy-type integral inequality; weight function; equivalent form; reverse; composition of operators;

D O I：

10.1186/s13660-015-0619-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By applying the way of real and functional analysis and estimating the weight functions, we build some lemmas and deduce some Hilbert-type and Hilbert-Hardy-type integral inequalities with the best possible constant factors. The equivalent forms, the reverses and the operator expressions are all considered. The composition formula of two Hilbert-Hardy-type integral operators and some examples are given.

引用

页数：18

共 20 条

[1] Half-discrete Hilbert-type inequalities with mean operators, the best constants, and applications [J].

Adiyasuren, Vandanjav ;

Batbold, Tserendorj ;

Krnic, Mario .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 231 :148-159

[2] On several new Hilbert-type inequalities involving means operators [J].

Adiyasuren, Vandanjav ;

Batbold, Tserendorj ;

Krnic, Mario .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (08) :1493-1514

[3]

Arpad B., 2006, J INEQUALITIES APPL, V2006, P28582

[4]

CARLEMAN T., 1923, Sur les equations integrales singulieres a noyau reel et symetrique

[5]

Fink A.M., 1991, MATH ITS APPL, V53

[6]

Hardy G.H., 1952, Inequalities

[7]

Hardy G.H., 1925, P LOND MATH SOC, V23, P45

[8] On a Multiple Hilbert-Type Integral Operator and Applications [J].

Huang, Qiliang ;

Yang, Bicheng .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2009,

[9]

KUANG J. C., 1996, Introduction to real analysis

[10]

Kuang JC., 2004, Applied inequalities, V4th ed

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