一个核带超几何函数的0次齐次的Hilbert型积分不等式

On a Hilbert-Type Integral Inequality with the Homogeneous Kernel of 0-Degree and the Hypergeometric Function

引进一个含独立参数的0次齐次核,通过实分析技巧估算权函数,建立了一个定义在全平面上的具有最佳常数因子的Hilbert型积分不等式,其中常数因子同时含有Beta函数和超几何函数.此外,还给出了逆向不等式及其相应的等价形式.

In this paper, by introducing a homogeneous kernel of 0-degree with an inde- pendent parameter and estimating the weight function through the real function techniques, a definition in the whole plane of the Hilbert-type integral inequality with a best constant factor is established, in which the best constant factor also contains Beta function and hy- pergeometric function. In addition, the reverse inequality and their corresponding equivalent forms are given.