| 一个新的Hibert型积分不等式及其逆 |
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| 引用本文： | 陈广生,丁宣浩. 一个新的Hibert型积分不等式及其逆[J]. 河南科技大学学报(自然科学版), 2011, 0(4): 90-94,113 |
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| 作者姓名： | 陈广生 丁宣浩 |
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| 作者单位： | 广西现代职业技术学院计算机工程系;重庆工商大学数学与统计学院; |
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| 基金项目： | 国家自然科学基金项目(10871217) |
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| 摘 要： | 通过引入独立参数λ,应用权函数方法和实分析技巧,研究了一类Hilbert型不等式,得到了一个新的Hilbert型积分不等式,证明了它的常数因子是最佳值.作为应用,建立了它的等价形式,并考虑其逆向不等式.
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| 关 键 词： | Hilbert型积分不等式 权函数 H(o)lder不等式 最佳常数因子 |
A New Hilbert-type Integral Inequality and Its Reverse |
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| CHEN Guang-Sheng,DING Xuan-Hao. A New Hilbert-type Integral Inequality and Its Reverse[J]. Journal of Henan University of Science & Technology:Natural Science, 2011, 0(4): 90-94,113 |
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| Authors: | CHEN Guang-Sheng DING Xuan-Hao |
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| Affiliation: | CHEN Guang-Sheng1,DING Xuan-Hao2(1.Department of Computer Engineering,Guangxi Modern Vocational Technology College,Hechi 547000,China,2.College of Mathematics & Statistics,Chongqing Technology & Business University,Chongqing 400067,China) |
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| Abstract: | A Hilbert’s type inequality was investigated by introducing independent parameter λ,using weight function and the method of real analisis.A new Hilbert-type integral inequality was obtained,and its constant factor was proved to be the optimum value.As its application,its equivalent form was built and its reverse inequalities was considered. |
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| Keywords: | Hilbert-type integral inequality Weight function Hlder inequality The best constant factor |
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