一个基本Hilbert型积分不等式的推广

A Generalization of Basic Hilbert-type Integral Inequality

利用权函数方法和实分析与泛函思想技巧,引入Γ-函数等特殊函数联合刻划常数因子,将一个基本Hilbert型积分不等式进行推广,考虑它的等价式,证明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 Γ- function and other special function to jointly score the constant factor,and using the way of weight function and the technic of real analysis and functional analysis,a basic Hilbert-type integral inequality is generalized. The equivalent form is considered and their constant factors are proved being the best possible,and some meaningful results are obtained by taking the special parameter values.