| 一个具有多参数的逆向Hilbert型不等式 |
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| 引用本文： | 陈广生,丁宣浩.一个具有多参数的逆向Hilbert型不等式[J].四川师范大学学报(自然科学版),2011,34(4):538-545. |
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| 作者姓名： | 陈广生 丁宣浩 |
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| 作者单位： | 1. 广西现代职业技术学院计算机工程系,广西河池,547000
2. 重庆工商大学数学与统计学院,重庆,400067 |
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| 基金项目： | 国家自然科学基金(10871217)资助项目 |
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| 摘 要： | 通过引入两个独立参数λ1,λ2和一对共轭指数(p,q),利用权函数方法和实分析技巧研究了双参数型的逆向Hilbert不等式,得到了一个多参数的、具有混合核的逆向Hilbert型积分不等式,并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及对应二重级数不等式.
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| 关 键 词： | Hilbert型积分不等式 权函数 Hlder不等式 最佳常数因子 |
A Reverse Hilbert-Type Inequality with Several Parameters |
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| CHEN Guang-sheng,DING Xuan-hao.A Reverse Hilbert-Type Inequality with Several Parameters[J].Journal of Sichuan Normal University(Natural Science),2011,34(4):538-545. |
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| Authors: | CHEN Guang-sheng DING Xuan-hao |
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| Institution: | CHEN Guang-sheng1,DING Xuan-hao2(1.Department of Computer Engineering,Guangxi Modern Vocational Technology College,Hechi 547000,Guangxi,2.College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067) |
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| Abstract: | A reverse Hilbert’s inequality of bi-parameter type is investigated by introducing two independent parameters λ1 and λ2 and one pairs of conjugate exponents(p,q),and by using weight function and the method of real analisis.A reverse Hilbert-type integral inequality with several parameters and a mixed kernel is obtained,and its constant factors is proved to be the optimum value.As application,an equivalent form and the corresponding to the double series inequalities are established. |
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| Keywords: | Hilbert type integral inequality weight function Hlder inequality the best constant factor |
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