Advances in Operator Theory

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

Michael Th Rassias and Bicheng Yang

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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.

Article information

Source
Adv. Oper. Theory, Volume 2, Number 3 (2017), 237-256.

Dates
Received: 1 March 2017
Accepted: 2 April 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431674

Digital Object Identifier
doi:10.22034/aot.1703-1132

Mathematical Reviews number (MathSciNet)
MR3730052

Zentralblatt MATH identifier
1371.26036

Subjects
Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 65B10: Summation of series

Keywords
hardy-type integral inequality weight function equivalent form Riemann zeta function operator

Citation

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


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