# Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function

Document Type: Original Article

Authors

Abstract

By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardy-type integral inequalities with the homogeneous kernel are deduced. We also consider the operator expressions.

Keywords

### Histroty

• Receive Date: 01 March 2017
• Revise Date: 30 March 2017
• Accept Date: 02 April 2017