一个联系超几何函数的齐次核Hilbert型积分不等式

A Homogeneous Kernel Hilbert-Type Integral Inequality Related to Hypergeometric Function

利用基于Hardy插值难题的权函数方法、一些实分析技巧和特殊函数的有关理论,引入了Γ-函数和超几何函数联合刻画不等式的常数因子,给出了一个具最佳常数因子的复合齐次核Hilbert型积分不等式,并考虑了其等价形式.作为应用,通过取一些满足结论条件的特殊参数值,不仅得到了参考文献中的有关结果,而且还能发现一些新的、形式简单的Hilbert型积分不等式.

In the weight function method based on the Hardy interpolation puzzle,some real analysis techniques and the special function related theories,and introducingΓ-function and the hypergeometric function to jointly characterize the constant factor of the inequality,a composite homogeneous kernel Hilbert-type integraline quality with the best constant factor has been given,and it's equivalent form been considered.As an application,by taking some special parameter values which satisfy the conclusion conditions,not only the relevant results in the references have been derived,but also some new Hilbert-type integral inequalities with simple form have been found.