On a multiple Hilbert-type integral inequality involving the upper limit functions

Abstract

Abstract By applying the weight functions, the idea of introducing parameters and the technique of real analysis, a new multiple Hilbert-type integral inequality involving the upper limit functions is given. The constant factor related to the gamma function is proved to be the best possible in a condition. A corollary about the case of the nonhomogeneous kernel and some particular inequalities are obtained.

Keywords

• Weight function
• Hilbert-type integral inequality
• Upper limit function
• Parameter
• Gamma function