A HALF-DISCRETE MULTIDIMENSIONAL HILBERT-TYPE INEQUALITY WITH THE GENERAL NONHOMOGENEOUS KERNEL AND A LOWER LIMIT FUNCTION

Abstract

By means of the weight functions, the idea of introduced parameters and Hardy's integral inequality, a new extended half-discrete multidimensional Hilbert-type inequality with the general nonhomogeneous kernel as well as one lower limit function is obtained. The equivalent statements of the best value in the new inequality related to several parameters are considered. The equivalent forms, the operator expressions and some particular cases are deduced.