A More Accurate Half-Discrete Multidimensional Hilbert-Type Inequality Involving One Multiple Upper Limit Function

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(x,λ>0) involving one multiple upper limit function is given, which is a new application of Hilbert-type inequalities. 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
• multiple upper limit function
• parameter
• beta function
• operator expression