A New Hardy–Hilbert-Type Integral Inequality Involving One Multiple Upper Limit Function and One Derivative Function of Higher Order

Abstract

Using weight functions and parameters, as well as applying real analytic techniques, we derive a new Hardy–Hilbert-type integral inequality with the homogeneous kernel 1(x+y)λ+n involving one multiple upper limit function and one derivative function of higher order. Certain equivalent statements of the optimal constant factor related to some parameters are considered. A few particular inequalities and the case of reverses are also provided.

Keywords

• weight function
• Hardy–Hilbert-type integral inequality
• multiple upper limit function
• derivative function of higher order
• parameter
• gamma function