一个新的Hilbert型积分不等式及其推广

A New Hilbert-type Integral Inequality and Its Generalization

通过估算权函数及引入Beta函数,应用实分析技巧,建立一个新的含参数的具有最佳常数因子的H ilbert型积分不等式.同时,建立了两种最佳推广式及其相应的等价形式.

By means of estimating the weight function and introducing the Beta function, and using the technical of real analysis, a new Hilbert-type integral inequality with a parameter and a best constant factor is established, and two best generalized forms of it and the corresponding equivalent forms are given.