一个新的涉及高阶导函数的半离散Hilbert型不等式

A New Half-Discrete Hilbert-Type Inequality InvolvingHigher-Order Derivative Function

用权函数的方法及实分析技巧,求出一个新的涉及高阶导函数的半离散Hilbert型不等式.作为应用,讨论了不等式中最佳常数因子联系多参数的等价条件及一些特殊不等式.

By using the method of weight functions and the technique of real analysis,we obtained a new half-discrete Hilbert-type inequality involving higher-order derivative function.As applications,we also discussed the equivalent conditions of optimal constant factor related to a few parameters in inequalities and some special inequalities.