一个双曲函数核Hilbert型不等式及应用

On a Hilbert-type inequality of the kernel with hyperbolic function and its applications

通过引进参数,构建一个全平面上的混合双曲函数核,建立了一个新的具有最佳常数因子的Hilbert型积分不等式。另外,利用余割函数的有理分式展开,建立了所得结果的特殊形式,并赋予参数特殊的数值,并给出了若干推论。

By introducing parameters, and constructing a kernel with mixed hyperbolic functions, we establish a new Hilbert-type integral inequality with the best constant factor. Moreover, by using the rational fraction expansion of cosecant function, a special case of the obtained result is presented. At last, by specifying the parameters with special values, we obtain some new conclusions.