| Hardy-Hilbert重级数定理的一个改进 |
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| 引用本文： | 周昱,高明哲.Hardy-Hilbert重级数定理的一个改进[J].数学理论与应用,2007,27(1):27-29. |
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| 作者姓名： | 周昱 高明哲 |
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| 作者单位： | 湖南吉首大学师范学院数学与计算机科学系 吉首416000 |
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| 基金项目： | 湖南省教育厅资助科研项目 |
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| 摘 要： | 利用Gram矩阵的正定性和Bernoulli不等式得到Holder不等式的一个加强的结果.由此建立了Hardy-Hilbert重级数定理的一个改进.特别,当p=2时,得到了经典的Hilbert重级数定理的一个很强的结果.
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| 关 键 词： | Gram矩阵 Bernoulli不等式 重级数 Hardy-Hilbert不等式 Hilbert不等式 |
| 文章编号： | 24259697 |
| 修稿时间： | 05 18 2006 12:00AM |
A Refinement of the Hardy - Hilbert Theorem for Double Series |
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| Zhou Yu ,Gao Mingzhe.A Refinement of the Hardy - Hilbert Theorem for Double Series[J].Mathematical Theory and Applications,2007,27(1):27-29. |
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| Authors: | Zhou Yu Gao Mingzhe |
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| Institution: | Department of Math. and Computer Science,Normal Collget,Jishou University,Hunan Jishou 416000 |
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| Abstract: | A strengthened result of Holder's inequality is attained by means of the positive definiteness of the Gram matrix and Bernoulli's inequality.Based on this,a refinement of Hardy-Hilbert's theorem for double series is built.In particular,for case p=2,a quite sharp result of the classical Hilbert theorem for double series is obtained. |
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| Keywords: | Gram matrix Bernoulli's inequality double series Hardy-Hilbert's inequality Hibert's inequality |
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