Equivalent properties of a reverse half-discrete Hilbert’s inequality

Abstract

Abstract By using the weight functions, the idea of introduced parameters and the Euler–Maclaurin summation formula, a reverse half-discrete Hilbert’s inequality with the homogeneous kernel and the reverse equivalent forms are given (for p<0 ${p<0}$, 0<q<1 ${0< q<1}$). The equivalent statements of the best possible constant factor related to a few parameters are considered. As applications, two corollaries about the case of the non-homogeneous kernel and some particular cases are obtained.

Keywords

• Weight function
• Half-discrete Hilbert’s inequality
• Parameter
• Euler–Maclaurin summation formula
• Reverse