## 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

Michael Th Rassias and Bicheng Yang

#### 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