一个参量化复合核Hilbert型积分不等式

A Hilbert-type integral inequality with multi-parameters and composite kernel

通过引入一些特殊函数来刻画常数因子,获得一个核为ln(1+e^(-αx^(λ_1)y^(λ_2)))的HardyHilbert型积分不等式,考虑了它的等价式,并证明了这对等价不等式的常数因子是最佳的.

By introducing some special functions to characterize the constant factor,a Hardy-Hilbert type integral inequality with the kernel ln（l ＋ e^-αx^λ1y^λ2） is obtained,and its equivalent form is considered.The constant factors of the equivalent inequalities are proved being the best possible.