关于一个零齐次核的Hilbert型积分不等式

On a Hilbert-type Integral Inequality with the Homogeneous Kernel of Degree 0

应用权函数的方法及实分析、复分析技巧,建立一个新的具有最佳常数因子的零齐次核为ln(xλ+byλ/xλ+ayλ)(λ>0,0<a<b)的Hilbert型积分不等式,还考虑了其等价式与相应逆式.关键词:权函数;Hilbert型积分不等式;

By using the way of weight functions and the techniques of real analysis and complex analysis,this paper presents a new Hilbert-type integral inequality with the homogeneous kernel of degree 0 as ln（xλ＋byλ/xλ＋ayλ）（λ0,0ab） and a best constant factor.The equivalent form and the reverses are also considered.