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关于多个函数的Hardy-Hilbert不等式的推广

Extensions of Hardy-Hilbert’s Inequality Involving Several Functions
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摘要 引入参数A,B,λ,建立了涉及多个函数的Hardy-Hilbert积分不等式,并考虑了它的等价形式及相应的级数不等式,并证明了当λ=1时,其常数因子是最佳的。 In this paper,by introducing parameters A,B,λ,the author gives a new extension of Hardy-Hilbert integral inequalities and Hardy-Hilbert double series inequalities involving several functions. It is proved that the constant factors are the best possible for λ=1.
作者 邢益冰 孙保炬
机构地区 浙江水利水电专科学校
出处 《科技通报》 北大核心 2009年第1期16-23,共8页 Bulletin of Science and Technology
关键词 Hardy-Hibert不等式 Hlder不等式 最佳常数因子 Hardy-Hilbert inequality H6lder inequality the best constant factors
分类号 O178 [理学—基础数学]
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参考文献6

  • 1KUANG Ji-chang. On new extensions of Hilbert's integral inequality [J ].Math Anal, & Appl, 1999,235:608-614.
  • 2HARDY G H, LITFLEWOOD J E, POLYA G. Inequalities [ M ].Gambridge University press, Gambridge, 1952.
  • 3HU Ke.On Hilbert's inequality [J ].Chinese Ann,Math. ,Ser.B, 1992,13( 1 ) :35-39.
  • 4GAO Ming-zhe,YANG Bi-cheng. On the extended Hilbert's inequality [J].Proceeding of the American Mathematical Society, 1998,126(3) :751-759.
  • 5YANG Bi-cheng, DEBNATH L. On the extended Hardy-Hilbert' s inequality [ J ].J. Math.Anal.Appl, 2002,272 ( 1 ) : 187-199.
  • 6杨必成.一个对偶的Hardy-Hilbert不等式及其推广(英文)[J].数学进展,2006,35(1):102-108. 被引量：5

二级参考文献8

  • 1Hardy,G.H.,Littlewood,J.E.,Polya,G.,Inequalities,Cambridge:Cambridge Univ.Press,
  • 2Yang Bicheng,On a generalization of Hilbert's double series theorem,Mathematical Inequalities and Applications,2002,5(2):197-204.
  • 3Gao Mingzhe,Wei Shongrong,He Leping,On the Hilbert inequality with weights,Journal for Analysis and its Applications,2002,21(1):257-263.
  • 4Mitrinovic,D.S.,Pecaric,J.E.,Fink,A.M.,Inequalities Involving Functions and Their Integrals and Derivatives,Boston:Kluwer Academic Publishers,1991.
  • 5Yang Bicheng,On a strengthened version of the more accurate Hardy-Hilbert's inequality,Acta Mathematica Sinica,1999,42(6):1103-1110.
  • 6Yang Bicheng,On a strengthened Hardy-Hilbert's inequality,J.Ineq.Pure.Appl.Math.,2000,1(2):Article 22.
  • 7Yang Bicheng,Debnath,L.,On a new generalization of Hardy-Hilbert's inequality and its applications,J.Math.Anal.Appl.,1999,233:484-497.
  • 8Kuang Jichang,Debnath,L.,On new generalizations of Hilbert's inequality and their applications,J.Math.Anal.Appl.,2000,245:248-265.

共引文献4

科技通报
2009年 第1期

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