关键词: Hilbert型积分不等式, 权函数, 最佳常数因子,  &Gamma, -函数,  &zeta, -函数, H\"{o}lder不等式, 结果

Abstract:

By introducing Γ-function and ζ-function, and using the way of weight function and the method of real analysis, a generalized Hilbert-type integral inequality is given. The equivalent form is considered and their constant factors are proved being the best possible. By taking the special parameter values, some meaningful results are obtained.

Key words: Hilbert-type integral inequality, Weight function, The best constant factor,  Γ-function,  ζ-function, H\"{o}lder’s inequality, Results