[1]有名辉.一个混合双曲函数核的Hilbert型不等式[J].温州大学学报(自然科学版),2020,(02):017-23.
 YOU Minghui.A Hilbert-type Inequality with the Mixed Kernel of Hyperbolic Functions[J].Journal of Wenzhou University,2020,(02):017-23.
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一个混合双曲函数核的Hilbert型不等式
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《温州大学学报》(自然科学版)[ISSN:1674-3563/CN:33-1344/N]

卷:
期数:
2020年02期
页码:
017-23
栏目:
数学
出版日期:
2020-05-25

文章信息/Info

Title:
A Hilbert-type Inequality with the Mixed Kernel of Hyperbolic Functions
作者:
有名辉
浙江机电职业技术学院数学教研室,浙江杭州 330053
Author(s):
YOU Minghui
Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou, China 330053
关键词:
Hilbert型不等式正割函数部分分式展开Gamma函数
Keywords:
Hilbert-type Inequality Secant Function Partial Fraction Expansion Gamma Function
分类号:
O178
文献标志码:
A
摘要:
通过引入参数,构造一个混合的双曲函数核,并借助权函数的方法,建立了一个定义在全平面上的Hilbert型积分不等式.特别地,利用正割函数的部分分式展开,得到了一个最佳常数因子与正割函数的高阶导数有关的Hilbert型不等式.最后,对参数赋予不同值,给出了一些特殊的Hilbert型不等式.
Abstract:
By introducing some parameters, this paper constructs a mixed kernel of hyperbolic functions, and, by using the method of weight function, establishes a Hilbert-type integral inequality defined in the whole plane. Particularly, through the partial fraction expansion of secant function, a special Hilbert-type inequality whose best constant factor is related to the higher derivative of secant function is also established. In addition, this paper obtains some meaningful Hilbert-type inequalities via giving different values to the parameters.

参考文献/References:

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相似文献/References:

[1]有名辉.一个含特殊常数因子的非齐次核Hilbert型不等式[J].温州大学学报(自然科学版),2016,(04):017.
 YOU Minghui.The Study of a Hilbert-Type Inequality Involving Non-homogeneous Kernel with Special Constant Factor[J].Journal of Wenzhou University,2016,(02):017.
[2]有名辉.一个全平面上非齐次核的Hilbert型不等式[J].温州大学学报(自然科学版),2019,(01):009.
 YOU Minghui.On Hilbert-type Inequality of Non-homogeneous Kernel in the Whole Plane[J].Journal of Wenzhou University,2019,(02):009.

备注/Memo

备注/Memo:
收稿日期:2019-08-12
基金项目:浙江省教育厅一般科研项目(Y201737260);浙江机电职业技术学院科教融合一般项目(A-0271-18-016)
作者简介:有名辉(1982- ),男,浙江安吉人,讲师,硕士,研究方向:解析不等式
更新日期/Last Update: 2020-05-25