Equivalent Statements of Two Multidimensional Hilbert-Type Integral Inequalities with Parameters

By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as H(||x||alpha lambda 1||y||beta lambda 2) (lambda 1,lambda 2 not equal 0) are given, which are some extensions of the Hilbert-type integral inequalities in the two-dimensional case. Some equivalent conditions of the best value and several parameters related to the new inequalities are provided. Two corollaries regarding the kernel, represented as k lambda(||x||alpha lambda 1,||y||beta lambda 2)(lambda 1,lambda 2 not equal 0), are given, and a few new inequalities for the particular parameters are obtained.