一个最佳常数为Beta函数的Hilbert型积分不等式

A Hilbert-type integral inequality with the best value of Beta function

运用估算权函数及实分析的方法,建立了一个新的核为|xλ1-yλ2|-a(0<a<1)的Hilbert型积分不等式及其等价形式.作为运用,证明了其常数因子为最佳值,并考虑了其含多独立参数的最佳推广形式及逆向的情形.

By using the way of weight function and the technique of real analysis,a new Hilbert-type integral inequality with a kernel ｜xλ1-yλ2｜-a（0a1）and its equivalent form are established.As application,the constant factor on the plane is the best value and its best extension form with some parameters and the reverse forms are also considered.