一个Hilbert型不等式及其等价形式的加强推广  

ON A STRENGTHENED AND GENERALIZED HILBERT-TYPE INEQUALITY AND ITS EQUIVALENT FORM

作　　者：黄启亮[1] 

机构地区：[1]广东教育学院数学系,广东广州510303

出　　处：《数学杂志》2010年第3期503-508,共6页Journal of Mathematics

基　　金：广东高校自然科学重点研究项目(05Z026);广东教育学院中青年骨干教师培养基金

摘　　要：本文研究了Hilbert型级数不等式.利用改进的Euler-Maclaurin求和公式及权系数的方法,并引进两对共轭指数,获得一个具有最佳常数系数的Hilbert型不等式,该不等式是联系若干Hilbert型不等式的加强推广式.作为应用,给出该不等式的等价形式及若干有意义的特殊结果.In this article,we study the Hilbert-type inequality.By using the improved Euler-Maclaurin＇s summation formula and estimating the weight coefficient and introducing two pairs of indexes of conjugate,we get a Hilbert-type inequality with a best constant coefficient which is a strengthened and generalized form of some early Hilbert-type inequalities.As applications,we also consider the equivalent form of this inequality and deal with some particulars.

关 键 词：HILBERT型不等式 等价形式 权系数 共轭指数 EULER-MACLAURIN求和公式 

分 类 号：O178[理学—数学]