一个经典Hilbert型积分不等式的推广

On an Extension of a Classical Hilbert-type Integral Inequality

通过引进参数,对一个经典的Hilbert型积分不等式的积分核函数进行推广,并由此建立一个新的Hilbert型不等式;然后,通过对建立的齐次型不等式进行变量代换,得到一个非齐次Hilbert型不等式;最后,对参数进行赋值,并借助余切函数的部分分式展开,给出新建立的不等式的特殊情形,推广了相关经典结果。

By introducing several parameters,the integral kernel function of a classical Hilbert-type integral inequality is extended,and a new Hilbert-type inequality is established.In addition,by variable substitution of the established homogeneous type inequality,a non-homogeneous Hilbert-type inequality is obtained.Finally,by specifying the values of parameters and using partial fraction expansion of the cotangent function,special cases of the newly-established inequality is given,and several classical results are generalized.