一个推广的Hilbert型积分不等式及其应用

AN EXTENSION OF THE HILBERT’S TYPE INTEGRAL INEQUALITY AND ITS APPLICATIONS

本文改进权函数的方法,引入参数λ,给一个Hilbert型积分不等式以具有最佳常数因子的推广.作为应用,建立其等价式及逆向形式.本文的结果及所提供的方法将对同类问题的研究起到有益的借鉴作用.

In this paper, by improvement of the way of weight function and introducing an independent parameter A, an extension of the Hilbert-type integral inequality with a best constant factor is given. As applications, the equivalent form and some reverses are considered. The results and the way in this paper provide an extensive amount for this type of inequalities.