EQUIVALENT CONDITIONS OF OPTIMAL HALF DISCRETE HILBERT TYPE MULTIPLE INTEGRAL INEQUALITIES WITH QUASI HOMOGENEOUS KERNEL AND APPLICATIONS.

Let G(u,v) be a λ-order homogeneous function. In this paper, by discussing optimal matching parameters of the half discrete Hilbert type multiple integral inequality with quasihomogeneous kernel K(n,||x||ρ,m) = G(nλ1,||x||λ2ρ,m), several equivalent conditions of the optimal matching parameters are obtained, and a basic theoretical problem of the half discrete Hilbert type inequality is solved. Finally, their applications to operator boundedness and operator norm are discussed. [ABSTRACT FROM AUTHOR]