The Equivalent Conditions of the Optimal Hilbert-Type Multiple Series Inequality with Quasi-Homogeneous Kernel

Abstract

By introducing several independent parameters, according to the structural symmetry of quasi-homogeneous kernels and the Hilbert-type inequality, and using the weight function method, the parameter conditions of the optimal Hilbert-type n-multiple series inequality with quasi-homogeneous kernels are discussed, and several equivalent conditions and the expression formula of the best constant factor are obtained. As applications, some special symmetric inequalities are given.