| 论全平面Hilbert型积分不等式及其算子刻画 |
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| 引用本文： | 杨必成.论全平面Hilbert型积分不等式及其算子刻画[J].广东教育学院学报,2014(5):1-23. |
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| 作者姓名： | 杨必成 |
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| 作者单位： | 广东第二师范学院数学系,广东广州510303 |
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| 基金项目： | 基金项目：国家自然科学基金资助项目（61370186）;2012年广东省高等院校学科建设专项资金项目（2012KJCX0079） |
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| 摘 要： | 引入独立参量,应用权函数的方法及实分析技巧,建立一个具有最佳常数因子的全平面非齐次核Hilbert型积分不等式,考虑了其等价式、逆式及相关的齐次式与Hardy型不等式;定义了全平面Hilbert型积分算子,还求出了一些特殊核的算子范数.
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| 关 键 词： | 权函数 全平面Hilbert型积分不等式 等价式 全平面Hilbert型积分算子 范数 |
On a Hilbert-Type Integral Inequality in the Whole Plane and Operator Expression |
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| YANG Bi-cheng.On a Hilbert-Type Integral Inequality in the Whole Plane and Operator Expression[J].Journal of Guangdong Education Institute,2014(5):1-23. |
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| Authors: | YANG Bi-cheng |
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| Institution: | YANG Bi-cheng (Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong, 510303, P. R. China) |
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| Abstract: | By introducing independent parameters, applying the way of weight functions and the technique of real analysis, a Hilbert-type integral inequality in the whole plane with a best possible constant factor and a non-homogeneous kernel is provided. The equivalent forms, the reverses, the related homogeneous homes and Hardy-type inequalities are considered. A Hilbert-type integral operator in the whole plane is defined, and the norms of operators for some particular kernels are obtained. |
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| Keywords: | weight function Hilbert-type integral inequality in the whole plane equivalent form Hilbert-type integral operator in the whole plane norm |
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