贺乐平,刘 妥
一个非齐次核的半离散型Hilbert型不等式的改进
贺乐平*,刘 妥
(吉首大学 数学与统计学院, 湖南 吉首, 416000)
式(1)称为Hardy-Hilbert积分不等式, 它在分析学中有重要的应用.
文献[1]给出了如下一个新的较精确的半离散Hilbert不等式:
为了方便起见, 先介绍一些符号:
证明见文献[2].
证明过程见文献[2].
为方便起见, 再引入一些符号:
证明 由引理1和引理2, 有:
即(5)式得证.
,
注: 式(5)即为式(2)的改进式.
[1] Yang Bicheng. A half-Discrete Hilbert-Type Inequality with a Non-Homogeneous kernel and two variables[J]. Mediterr J Math, 2012(12): 213—218.
[2] He Leping, Gao Mingzhe, Jia weijian. On a New Strengthened Hardy-Hilbert’sInequality[J]. Journal of Mathematical Research and Exposition, 2006, 26(2): 276—282.
[3] He Leping, Gao Mingzhe. A Hilbert Integral Inequality with Hurwitz Zeta Function[J]. Journal of Mathematical inequalities, 2013, 7(3): 377—387.
Improvement of half-discrete Hilbert-type inequality with non-homogeneous kernel
HE LePing, LIU Tuo
(College of Mathematics and Statistics, Jishou University, Jishou 416000, China)
Hilbert-type inequality are important in analysis and its applications. In this paper, a half-discrete Hilbert-type inequality is investigated. By using the way of weight functions and the techniuque of real analysis and a sharpening of Hölder’s inequality, some improvements of Hardy-Hilbert’s inequality are given, a few new inequalities are established.
O 178
1672-6146(2014)01-0001-03
10.3969/j.issn.1672-6146.2014.01.001
通讯作者email: jdlepinghe@163.com.
2014-01-08
国家自然科学基金资助项目(11261020)
(责任编校:刘晓霞)