| 一个多参数的Hilbert型积分不等式 |
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| 引用本文： | 刘琼.一个多参数的Hilbert型积分不等式[J].吉林大学学报(理学版),2009,47(5):903-908. |
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| 作者姓名： | 刘琼 |
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| 作者单位： | 邵阳学院 理学与信息科学系, 湖南 邵阳 422000 |
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| 摘 要： | 通过引入参数λ1,λ2, 利用权函数方法和实分析技巧研究双参数型Hilbert不等式, 得到了一个多参数的Hilbert型积分不等式及其等价式, 证明了它们的常数因子是最佳值, 并通过在结果中选取符合条件的合适参数, 得到了一系列形式简洁的Hilbert型积分不等式.
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| 关 键 词： | Hilbert型积分不等式 参数 权系数 最佳常数因子 Hlder不等式 应用 |
| 收稿时间： | 2008-11-25 |
A Hilbert-type Integral Inequality with Several Parameters |
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| LIU Qiong.A Hilbert-type Integral Inequality with Several Parameters[J].Journal of Jilin University: Sci Ed,2009,47(5):903-908. |
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| Authors: | LIU Qiong |
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| Institution: | Department of Science and Information Science, Shaoyang University, Shaoyang 422000, Hunan Province, China |
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| Abstract: | A Hilbert’s inequality of bi parameter type wasinvestigated by introducing the parameters: λ1,λ2, and using the way of weight coefficient and the method of real analysis. A Hilbert type integral inequality with several parameters and its equivalent form were obtained, and their constant factors were proved to be the optimum value. A series of Hilbert’s type integral inequalities with more simple forms were obtained via selecting the appropriate parameters satisfying the conditions selected in the results. |
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| Keywords: | Hilbert type integral inequality parameter weight coefficient the best constant factor Hlder’s inequality application |
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