一个核含对数函数的Hilbert型积分不等式

On a Hilbert-Type Integral Inequality with the Kernel Containing Logarithm Function

应用实分析、复分析技巧及权函数方法,建立一个新的具有最佳常数因子的核为对数函数ln(1+bxδλyλ/1+axδλyλ)(λ>0,0<a<b,δ∈{-1,1})的Hilbert型积分不等式,还导出了其等价式及特殊参数δ=-1下的齐次形式.

By using the technique of real analysis, complex analysis and the way of weight functions, a new Hilbert-type integral inequality with the Logarithm kernel ln（1＋bxδλyλ/1＋axδλyλ）（λ〉0,00〈a〈b,δ∈{-1,1}）and a bestconstant factor are given. The equivalent form and the homogeneous forms for the particular parameter δ = - 1 are considered.