Equivalent conditions and applications of a class of Hilbert-type integral inequalities involving multiple functions with quasi-homogeneous kernels

摘要

Let K(x1, …, xn) satisfy K(x1,…,txi,…,xn)=tλλiK(t−λiλ1x1,…,xi,…,t−λiλnxn) for t  0. With this integral kernel, by using the method and technique of weight coefficients, the equivalent conditions and the best constant factors for the validity of Hilbert-type integral inequalities involving multiple functions are discussed. Finally, the applications of the integral inequalities are considered.