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

Let K ( x 1 , … , x n ) satisfy K ( x 1 , … , t x i , … , x n ) = t λ λ i K ( t − λ i λ 1 x 1 , … , x i , … , t − λ i λ n x n ) 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.