WU Weiliang.A Hilbert-type integral inequality with the best value of Beta function[J].Journal of Yanbian University,2014,40(02):100-103.
一个最佳常数为Beta函数的Hilbert型积分不等式
- Title:
- A Hilbert-type integral inequality with the best value of Beta function
- 关键词:
- 权函数; Hilbert型积分不等式; 最佳推广; 逆式
- 分类号:
- O178
- 文献标志码:
- A
- 摘要:
- 运用估算权函数及实分析的方法,建立了一个新的核为|xλ1-yλ2|-a(0<a<1)的Hilbert型积分不等式及其等价形式.作为运用,证明了其常数因子为最佳值,并考虑了其含多独立参数的最佳推广形式及逆向的情形.
- Abstract:
- By using the way of weight function and the technique of real analysis, a new Hilbert-type integral inequality with a kernel |xλ1-yλ2|-a(0<a<1)and its equivalent form are established. As application, the constant factor on the plane is the best value and its best extension form with some parameters and the reverse forms are also considered.
参考文献/References:
[1] Hardy G H. Note on a theorem of Hilbert concerning series of positive terms[J]. Proc LondonMath Soc, 1925,23(2):XLV-XLVL.
[2] Hardy G H, Littewood J E, Polya G. Inequalities[M]. Cambridge: Cambridge University Press, 1952:226-236.
[3] Mitrinovic D S, Pecaric J, Fink A M. Inequalities Involving Functions and Their Integrals and Derivatives[M ]. Boston: Kluwer Academic Publishers, 1991:108-132.
[4] 杨必成.参量化的Hilbert不等式[J].数学学报,2006,49(5):1121-1126.
[5] Xu Jingshi. Hardy-Hilbert’s inequalities with two parameters[J]. Advancesin Mathematics, 2007,36(2):63-76.
[6] Yang Bicheng. On the norm of an integral operator and applications[J]. J Math Anal Appl, 2006,321:182-192.
[7] 巫伟亮.一个含多独立参数的新Hilbert型积分不等式及其应用[J].西北师范大学学报:自然科学版,2012,48(6):26-30.
[8] 杨必成.一个新的Hilbert 型不等式及其推广[J].吉林大学学报:理学版,2005,43(5):580-584.
[9] 匡继昌.常用不等式[M].济南:山东科学技术出版社,2004:12-19.
[10] 周民强.实变函数论[M].北京:北京大学出版社,2008:156-185.
备注/Memo
收稿日期: 2013-11-21 作者简介: 巫伟亮(1983—),男,讲师,研究方向为解析不等式、抛物型偏微分方程.基金项目: 国家自然科学基金资助项目(61370186); 嘉应学院育苗工程项目(2012KJM02)