| 两个新的积分不等式和一个算子范数关系式 |
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| 作者姓名： | 刘琼 |
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| 作者单位： | 邵阳学院理学与信息科学系, 湖南 邵阳 422000 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11171280) and Scientific Support Project of Hunan Education Department(10C1186) |
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| 摘 要： | 利用权函数方法和拉普拉斯积分变换, 给出2个新的积分不等式和它们的等价式, 证明它们的常数因子是最佳的. 作为应用, 一方面通过选取一些特殊参数值, 获得一些有意义的结果;另一方面定义3个积分算子, 建立它们之间的一个范数关系式.
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| 关 键 词： | 积分不等式 权函数 拉普拉斯积分变换 最佳常数因子 算子范数 |
| 收稿时间： | 2014-03-24 |
| 修稿时间： | 2014-05-22 |
Two new integral inequalities and a relationship among operator norms |
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| Authors: | LIU Qiong |
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| Institution: | Department of Science and Information, Shaoyang University, Shaoyang 422000, Hunan, China |
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| Abstract: | By means of weight function and Laplace's integral transform, two new integral inequalities and their equivalent forms are given, and their constant factors are proved being the best possible. Some meaningful results are obtained by selecting the special parameter values. Three integral operators are defined, and a relation among their norms is established. |
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| Keywords: | integral inequality weight function Laplace's integral transform the best constant factor operator norm |
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