一个涉及高阶导函数的Hardy-Hilbert型积分不等式

A Hardy-Hilbert-type Integral Inequality Involving the Derivative Functions of Higher-order

应用权函数方法、参量化思想及实分析技巧,建立一个新的齐次核为1/(x+y)^(λ+m+n)(λ>0)的涉及高阶导函数的Hardy-Hilbert型积分不等式,求出了联系该式的最佳常数因子及多参数的等价陈述.作为推论,还求出了特殊条件下该不等式的等价形式、非齐次核的情形及算子表示,并导出了若干特例.

By means of the weight functions,the idea of introducing parameters and the technique of real analysis,a new Hardy-Hilbert-type integral inequality with the homogeneous kernel as 1/(x+y)^(λ+m+n)(λ>0)involving the derivative functions of higher-order is given.The equivalent statements of the best possible constant factor related to several parameters are considered.As corollaries,the equivalent forms,the case of nonhomogeneous kernel and the operator expressions in a condition are provided,and some particular inequalities are obtained.