| 一个新的实齐次核的Hilbert型积分不等式及其等价形式 |
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| 引用本文： | 谢子填,曾峥,周庆华.一个新的实齐次核的Hilbert型积分不等式及其等价形式[J].吉林大学学报(理学版),2012,50(4):693-697. |
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| 作者姓名： | 谢子填 曾峥 周庆华 |
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| 作者单位： | 1. 广东肇庆学院 数学系, 广东 肇庆 526061,2. 韶关学院 数学系, 广东 韶关 512005 |
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| 摘 要： | 通过引入双参数的实齐次核, 应用权函数方法给出一个新的有最佳常数因子的Hilbert型积分不等式及其等价形式, 并证明了常数因子的最佳性, 它与ψ函数有关. 同时, 给出了逆向不等式及相应的等价形式.关键词: Hilbert积分不等式; 权函数; Hlder不等式; ψ函数中图分类号: O178文献标志码： A文章编号： 1671-5489(2012)04-0693-05
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| 关 键 词： | ,Hilbert积分不等式,权函数,Hlder不等式,ψ函数, |
| 收稿时间： | 2011-10-09 |
A New Hilbert-Type Integral Inequality with the Homogeneous Kernel of Real Number-Degree and Its Equivalent Forms |
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| XIE Zi-tian
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ZENG Zheng
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ZHOU Qing-hua.A New Hilbert-Type Integral Inequality with the Homogeneous Kernel of Real Number-Degree and Its Equivalent Forms[J].Journal of Jilin University: Sci Ed,2012,50(4):693-697. |
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| Authors: | XIE Zi-tian ZENG Zheng ZHOU Qing-hua |
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| Institution: | 1. Department of Mathematics, Zhaoqing University, Zhaoqing 526061, Guangdong Province, China;
2. Department of Mathematics, Shaoguan University, Shaoguan 512005, Guangdong Province, China |
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| Abstract: | Having introduced a homogeneous kernel of real number-degree with two independent parameters and estimating the weight function,we gave a new Hilbert-type integral inequality with a real number-degree with a best constant factor,it involves the equivalent inequality with reverse forms considered.It involves the ψ function.The reverse inequality and their corresponding equivalent forms were given. |
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| Keywords: | Hilbert-type integral inequality weight function Hlder’s inequality ψ function |
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