EQUIVALENT PROPERTIES OF A HILBERT-TYPE INTEGRAL INEQUALITY WITH THE BEST CONSTANT FACTOR RELATED TO THE HURWITZ ZETA FUNCTION

被引：19

作者：

Rassias, Michael ^{[1
,2
]}

Yang, Bicheng ^{[3
]}

机构：

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[2] Inst Adv Study, Program Interdisciplinary Studies, 1 Einstein Dr, Princeton, NJ 08540 USA

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

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2018年 / 9卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Hilbert-type integral inequality; weight function; Hurwitz zeta function; equivalent form; operator;

D O I：

10.1215/20088752-2017-0031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By the use of methods of real analysis and weight functions, we study the equivalent properties of a Hilbert-type integral inequality with the nonhomogeneous kernel. The constant factor related to the Hurwitz zeta function is proved to be the best possible. As a corollary, a few equivalent conditions of a Hilbert-type integral inequality with the homogeneous kernel are deduced. We also consider their operator expressions.

引用

页码：282 / 295

页数：14

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