有最佳常数的Hilbert型不等式的推广  

A Generalization of a Hilbert-type Inequality with the Best Constant Factor

作　　者：谢子填[1] 周方敏[1] 

机构地区：[1]肇庆学院数学系,广东肇庆526061

出　　处：《四川师范大学学报（自然科学版）》2009年第5期626-629,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：广东省自然科学基金(06025059)资助项目

摘　　要：Hilbert型不等式在分析中有重要作用,近年来,由于改进权系数的方法,发展了这类不等式,并进一步推广应用和研究,应用权系数方法给出的一个带有最佳常数的核为负二次型齐次的Hibert型无穷级数不等式,同时考虑了它的等价形式.Hilbet-type inequality is important in analysis and its applications. In recent years,by improving the way of weight coefficient,some research on the extensions and applications of this type of inequalities are developed. In this paper,we give a Hilbert infinite series inequality with the best constant factor whose kernel is a negative quadratic form by applying the method of weight coefficients. And an equivalent form is considered.

关 键 词：HILBERT不等式 权系数 HLDER不等式 

分 类 号：O173[理学—数学]