一个参量化复合核Hilbert型积分不等式

摘要 通过引入一些特殊函数来刻画常数因子,获得一个核为\,$\ln(1+\mathrm{e}^{-\alpha x^{\lambda_1}y^{\lambda_2}})$\,的\,Hardy-Hilbert\,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.
Abstract：By introducing some special functions to characterize the constant factor, a Hardy-Hilbert type integral inequality with the kernel $\ln(1+\mathrm{e}^{-\alpha x^{\lambda_1}y^{\lambda_2}})$ is obtained, and its equivalent form is considered. The constant factors of the equivalent inequalities are proved being the best possible.