一个全平面上多参数的Hilbert型不等式

On A Hilbert-Type Inequality in the Whole Plane with Multi-Parameters

通过引进参数,构造一个定义在全平面上的积分核函数,利用正割函数的有理分式展开,建立一个常数因子与正割函数高阶导数有关的Hilbert型积分不等式.另外,赋予结论中的参数不同的值,文中还给出了一些特殊结果.

By introducing parameters,we construct a new kernel function involving hyperbolic functions in the whole plane,an by using the rational fraction expansion of secant function,a Hilbert-type integral inequality with the constant factor related to the higher derivative of secant function is established.In addition,giving the parameters different values,some meaningful Hilbert-type inequalities are obtained.