Abstract: By using the weight function method, the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K ( n,||x|| _ρ,m ) = G ( n ^{λ 1} ||x|| ^{λ 2}_ρ,m ) are discussed, some equivalent conditions of the optimal matching parameter are established, and the expression of the optimal constant factor is obtained. Finally, their applications in operator theory are considered.

Key words: Non-homogeneous kernel, Half discrete Hilbert type multiple integral inequality, Best constant factor, Optimal matching parameter, Operator norm, Bounded operator