| 一个R2上含双曲函数核的Hilbert型不等式 |
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| 引用本文： | 有名辉,孙霞.一个R2上含双曲函数核的Hilbert型不等式[J].浙江大学学报(理学版),2021,47(5):554-558. |
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| 作者姓名： | 有名辉 孙霞 |
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| 基金项目： | 浙江机电职业技术学院科教融合一般项目(A-0271-20-007). |
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| 摘 要： | 通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。
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| 关 键 词： | Hilbert型不等式 正切函数 双曲函数 有理分式展开 Gamma函数 |
| 收稿时间： | 2019-08-13 |
A Hilbert-type inequality defined on R2 with the kernel involving hyperbolic functions |
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| YOU Minghui,SUN Xia.A Hilbert-type inequality defined on R2 with the kernel involving hyperbolic functions[J].Journal of Zhejiang University(Sciences Edition),2021,47(5):554-558. |
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| Authors: | YOU Minghui SUN Xia |
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| Institution: | Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China |
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| Abstract: | By introducing some parameters, we construct a non-homogeneous kernel function including hyperbolic functions on the whole plane. In addition, by using the rational fraction expansion of tangent function, a Hilbert-type integral inequality associated with the best possible constant factor and the higher derivatives of tangent function is presented. Furthermore, some meaningful and special results are presented by specializing the parameters with different values as on application. |
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| Keywords: | Hilbert-type inequality tangent function hyperbolic function rational fraction expansion Gamma function |
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