两个新的Hilbert型积分不等式

Two New Hilbert-type Integral Inequality

引入独立参量及运用估算权函数的方法,建立了一个新的半平面Hilbert型积分不等式;进一步引入指数函数为中间变量,得到了一个全平面的Hilbert型积分.作为应用,考虑了它们的等价形式及常数因子的最佳性.

By introducing the independent parameters and using the method of estimation of weight function, a new Hilbert-type integral inequality in the half plane is established. Furthermore, by introducing interval variables, a Hilberttype integral inequality in the whole plane is obtained.As applications, their equivalent forms and the best possible constant factors are considered.