WU Weiliang.A Hilbert-type integral inequality with the best value as logarithm[J].Journal of Yanbian University,2015,41(02):129-131.
一个最佳值为对数的Hilbert型积分不等式
- Title:
- A Hilbert-type integral inequality with the best value as logarithm
- 关键词:
- Hilbert型积分不等式; 权函数; 等价式; 最佳值
- 分类号:
- O178
- 文献标志码:
- A
- 摘要:
- 运用参量化思想、估算权函数方法及实分析技巧,建立了一个新的核为(min{1,xδ λyλ})/(1+xδ λy+max{1,xδ λyλ})(λ>0, δ∈{1,-1})的Hilbert型积分不等式及其等价形式,并证明了它们的常数因子为最佳值,同时得到了该不等式的一些应用.
- Abstract:
- By using the though of parametrization, applying the way of weight coefficient and the technique of real analysis, a new Hilbert-type integral inequality with a kernel of independent parameters(min{1,xδ λyλ})/(1+xδ λy+max{1,xδ λyλ})(λ>0, δ∈{1,-1})and its equivalent form are established. Their constant factor is proved to be the best value and its application is given.
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备注/Memo
收稿日期: 2015-02-26 作者简介: 巫伟亮(1983—),男,博士,讲师,研究方向为解析不等式和偏微分方程.基金项目: 广东省自然科学基金博士启动项目(S2013040015141); 嘉应学院科研重点项目(2012KJZ02)