Abstract:

In this paper, by using the way of weight function and the technique of real analysis, and introducing some parameters and some special functions to jointly characterize the constant factor, a multi-parameters Hilbert-type integral inequality is given. It's equivalent form is considered and their constant factors are proved being the best possible. At the same time, a useful multi-parameters integral inequality with the kernel of hyperbolic cotangent function is obtained.

Key words: Integral inequality, Weight function, The best constant factor, Multi-parameters, Special function