A Multidimensional Half-Discrete Hardy-Hilbert s Inequality Involving One Partial Sum

In this paper, by using weight functions, the idea of introduced parameters, and techniques of real analysis, a multidimensional half-discrete Hardy–Hilbert inequality with a new kernel of the form 1 / (u(m) + ||y||_β^α)^λ (α > 0, λ > 0) involving one partial sum is obtained. The equivalent statements of the best values related to the parameters are considered, and some corollaries are deduced.