A Hilbert-Type Integral Inequality with Multiparameters and a Nonhomogeneous Kernel

Abstract

We first introduce $\mathrm{\Gamma }$-function and Riemann $\mathrm{\zeta }$-function to characterize the constant factor jointly. A Hilbert-type integral inequality with multiparameters and a nonhomogeneous kernel is given using the way of weight function and the technique of real analysis. The equivalent form is considered and its constant factors are proved to be the best possible. Some meaningful results are obtained by taking the special parameter values.