| 一个引入中间变量的一般非齐次核全平面Hilbert型积分不等式 |
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| 引用本文： | 廖建全,杨必成.一个引入中间变量的一般非齐次核全平面Hilbert型积分不等式[J].数学学报,2020,63(1):27-44. |
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| 作者姓名： | 廖建全 杨必成 |
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| 作者单位： | 广东第二师范学院数学系 广州 510303 |
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| 基金项目： | 国家自然科学基金青年科学基金资助项目（11401113）；广东省2017年重点平台及科研项目—特色创新类项目（自然科学）（2017KTSCX133） |
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| 摘 要： | 应用实分析及权函数的方法,引入一些参数及中间变量,建立一个一般非齐次核全平面Hilbert型积分不等式的若干等价陈述.常数因子被证明是最佳的.作为应用,一个一般齐次核全平面Hilbert型积分不等式的若干等价陈述被导出.我们还考虑了一些特殊情况、算子表示及若干例子.
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| 关 键 词： | Hilbert型积分不等式 权函数 中间变量 等价形式 算子 |
On a Hilbert-Type Integral Inequality with the General Nonhomogeneous Kernel and the Intermediate Variables in the Whole Plane |
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| Jian Quan LIAO,Bi Cheng YANG.On a Hilbert-Type Integral Inequality with the General Nonhomogeneous Kernel and the Intermediate Variables in the Whole Plane[J].Acta Mathematica Sinica,2020,63(1):27-44. |
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| Authors: | Jian Quan LIAO Bi Cheng YANG |
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| Institution: | Department of Mathematics, Guangdong University of Education, Guangzhou 510303, P. R. China |
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| Abstract: | By means of the way of real analysis and the weight functions, introducing some parameters and intermediate variables, a few equivalent statements of a Hilberttype integral inequality with the general nonhomogeneous kernel in the whole plane are obtained. The constant factor is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the general homogeneous kernel in the whole plane are deduced. We also consider some particular cases, the operator expressions and a few examples. |
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| Keywords: | Hilbert-type integral inequality weight function intermediate variable equivalent form operator |
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