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

Abstract

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 − ξ ∥ α ) λ + m ( x , λ > 0 ) $\frac{1}{(x + \Vert k - \xi \Vert _{\alpha} )^{\lambda + m}}\ (x,\lambda > 0)$ 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.

Keywords

• Weight function
• Half-discrete multidimensional Hilbert-type inequality
• Derivative function of m-order
• Parameter
• Beta function