通过引入多个参数,应用权函数方法、实分析技巧和拉普拉斯积分变换, 给出一个参量化Hilbert型积分不等式及其等价式, 证明它们的常数因子是最佳的. 作为应用, 通过选取一些特殊参数值, 获得了一些有意义的结果.
By introducing some parameters and by using the way of weight function and the techniques of real analysis and Laplace's integral transform, a parametric Hilbert-type integral inequality and its equivalent form are given, and their constant factors are proved to be the best values. As applications, some meaningful results are obtained by selecting the special values for the parameters.
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