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一个半离散非齐次核的Hilbert不等式 被引量：7

A Half-Discrete Hilbert's Inequality with a Non-Homogeneous Kernel
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摘要 应用权系数的方法及参量化思想,建立一个推广的具有最佳常数因子的、半离散且含一对共轭指数及单参数非齐次核的Hilbert不等式,并考虑了它的等价式与逆式. By using the method of weight coefficient and the idea of introducing parameters,an extended half-discrete Hilbert＇s inequality with a best constant factor,a pair of conjugate exponents as well as a parameter,and a non-homogeneous kernel is given.Its equivalent forms and some reverses are also considered.
作者 杨必成
机构地区 广东第二师范学院数学系
出处 《湛江师范学院学报》 2011年第6期5-12,共8页 Journal of Zhanjiang Normal College
基金 广东省自然科学基金资助项目(7004344)
关键词 权系数 参数 HILBERT型不等式 等价式 逆式 weight coefficient parameter Hilbert＇s inequality equivalent form reverse
分类号 O178 [理学—基础数学]
  • 相关文献

参考文献10

  • 1HARDY G H, LITTLEWOOD J E, POLYA G. Inequalities [M]. Cambridge: Cambridge University Press, 1952.
  • 2MINTRINOVICE D S, PECARIC J E, FINK A M. Inequalities involving functions and their integrals and derivatives [M]. Boston: Kluwer Academic Publishers, 1991.
  • 3YANG Bi--cheng. Hilbert--type integral inequalities [M]. Dubai: Bentham Science Publishers Ltd, 2009.
  • 4YANG Bi--cheng. Discrete Hilbert--type inequalities [M]. Dubai: Bentham Science Publishers Ltd, 2011.
  • 5KRNIC M, PECARIC J. Hilbert's inequalities and their reverses [J].Publ Math Debrecen, 2005, 67(3/4):315--331.
  • 6AZAR L. On some extensions of Hardy-- Hilbert" s inequality and applications [J]. Journal of Inequalities and Applications,2009, no. 546829.
  • 7杨必成.一个半离散且正数齐次核逆向的Hilbert型不等式[J].湛江师范学院学报,2011,32(3):5-9. 被引量：17
  • 8杨必成.一个半离散的Hilbert不等式[J].广东第二师范学院学报,2011,31(3):1-7. 被引量：59
  • 9YANG Bi--cheng. A mixed Hilbert--type inequality with a best constant factor [J]. International Journal of Pure and Applied Mathematics, 2005, 20(3) : 319--328.
  • 10YANG Bi cheng. On Hilbert's integral inequality [J]. Journal of Mathematical Analysis and Applications, 1998, 220: 778--785.

二级参考文献8

  • 1YANG Bi-cheng.Hilbert-type integral inequalities. . 2009
  • 2YANG Bi-cheng.Discrete Hilbert-type inequalities. . 2011
  • 3Hardy GH,Littlewood JE,Polya G.Inequalities. . 1952
  • 4Mitrinovic DS,Pecaric JE,Fink AM.Inequalities involving functions and their integrals and derivatives. . 1991
  • 5YANG Bi-cheng.A mixed Hilbert-type inequality with a best constant factor. International Jour-nal of Pure and Applied Mathematics . 2005
  • 6YANG Bi-cheng.On Hilbert’’s integral inequality. Journal of Mathematical Analysis and Applica-tions . 1998
  • 7杨必成.关于正数齐次核的Hilbert型不等式[J].广东教育学院学报,2009,29(3):1-8. 被引量：18
  • 8杨必成.A Note on HilbertsIntegral Inequalities[J].Chinese Quarterly Journal of Mathematics,1998,13(4):83-86. 被引量：51

共引文献59

同被引文献60

  • 1钟玉泉.复变函数论[M].北京:高等教育出版社,2005.
  • 2HARDY G H, LITTLEWOOD J E, POLYA G. Inequalities [M]. Cambridge. Cambridge University Press, 1952.
  • 3MINTRINOVICE D S, PECARIC J E, FINK A M. Inequalities involving functions and their integrals and derivatives [M]. Boston. Kluwer Academic Publishers, 1991.
  • 4YANG Bi-cheng. Hilbert-type integral inequalities [M]. Bentham Science Publishers Ltd, 2009.
  • 5YANG Bi-cheng. Discrete Hilbert-type inequalities [M]. Bentham Science Publishers Ltd, 2011.
  • 6YANG Bi-eheng. On Hilbert's integral inequality [J]. Journal of Mathematical Analysis and Applica- tions, 1998, 220: 778-785.
  • 7YANG Bi-cheng. A mixed Hilbert-type inequality with a best constant factor[J]. International Jour- nal of Pure and Applied Mathematics, 2005, 20(3). 319-328.
  • 8YANG Bi-cheng, CHEN Qiang. A half-discrete Hilbert-type inequality with a homogeneous kernel and an extension[J]. Journal of Inequalities and Applications,2011:124.
  • 9HE Bing, YANG Bi-cheng. On a half-discrete inequality with a generalized homogeneous kernel [J]. Journal of Inequalities and Applications, 2012 : 30.
  • 10Hardy. G H, Littlewood J E, Polya G. Inequalities [M]. Cambridge: Cambridge University Press, 1952.

引证文献7

二级引证文献11

湛江师范学院学报
2011年 第6期

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