一个含多参数全平面的Hilbert型积分不等式

A Hilbert-type Integral Inequality on the Plane with Some Parameters

通过引入a,λ,σ等独立参量及Beta函数,运用估算权函数的方法及实分析的技巧,建立全平面上一个新的非齐次核为1/|1-axy|~σ(a≥1)的Hilbert型积分不等式,证明了其常数因子是最佳值并考虑了其等价形式。

Introducing a,λ,σ some independent parameters and the Beta function, and using the way of weight coefficient and the technique of real analysis, a new Hilbert -type integral inequality with non -homogeneous kernel as 1 1-axy σ （a≥1） on the plane was given. The constant factor is the best and its equivalent form is also established.