On a more accurate half-discrete multidimensional Hilbert-type inequality involving one derivative function of m-order

Abstract By means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with the homogeneous kernel as 1 (x + k - _{) ^ + m}\ (x, > 0) 1 (x + ∥ k − ξ ∥ α) λ + m (x, λ > 0) involving one derivative function of m-order is given. The equivalent conditions of the best possible constant factor related to several parameters are considered. The equivalent forms. the operator expressions and some particular inequalities are obtained.