Advances in Operator Theory
- Adv. Oper. Theory
- Volume 2, Number 3 (2017), 237-256.
Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function
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.
Adv. Oper. Theory, Volume 2, Number 3 (2017), 237-256.
Received: 1 March 2017
Accepted: 2 April 2017
First available in Project Euclid: 4 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 65B10: Summation of series
Rassias, Michael Th; Yang, Bicheng. Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function. Adv. Oper. Theory 2 (2017), no. 3, 237--256. doi:10.22034/aot.1703-1132. https://projecteuclid.org/euclid.aot/1512431674