一个推广的Hilbert型积分不等式

A Generalization of Hilbert-type Integral Inequality

引入Γ-函数和ζ-函数,利用权函数方法和实分析技巧,建立一个推广的Hilbert型积分不等式.考虑了它的等价式,证明了它们的常数因子是最佳的,并通过取特殊的参数值,得到一些有意义的结果.

By introducing Г-function and ζ-function, and using the way of weight function and the method of real analysis, a generalized Hilbert-type integral inequality is given. The equivalent form is considered and their constant factors are proved being the best possible. By taking the special parameter values, some meaningful results are obtained.