逆向Hilbert型积分不等式的一组等价陈述

A Group of Equivalent Statements of the Reverse Hilbert-Type Integral Inequality

应用实分析及权函数的方法,探讨非齐次核逆向Hilbert型积分不等式的一组等价陈述,及常数因子最佳性的条件.作为推论,考虑了齐次核及一些特殊参数的等价式的情形.还给出了若干最佳常数因子联系着推广的Hurwitz zeta函数的不等式的例子.

By using the way of real analysis and weight functions,we study a group of equivalent statements of the reverse Hilbert-type integral inequality with the non-homogeneous kernel and the conditions of the inequalities which possess the property of the best possible constant factor. As corollaries,the case related to the homogeneous kernel and some particular parameters are also considered. Moreover,a few examples related to the extended Hurwitz zeta function are obtained.