A FEW EQUIVALENT STATEMENTS OF A HILBERT-TYPE INTEGRAL INEQUALITY WITH THE RIEMANN-ZETA FUNCTION

Weiliang Wu; Bicheng Yang

doi:10.11948/20190238

2020 Volume 10 Issue 6

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Weiliang Wu, Bicheng Yang. A FEW EQUIVALENT STATEMENTS OF A HILBERT-TYPE INTEGRAL INEQUALITY WITH THE RIEMANN-ZETA FUNCTION[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2400-2417. doi: 10.11948/20190238

Citation:

Weiliang Wu, Bicheng Yang. A FEW EQUIVALENT STATEMENTS OF A HILBERT-TYPE INTEGRAL INEQUALITY WITH THE RIEMANN-ZETA FUNCTION[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2400-2417. doi: 10.11948/20190238

A FEW EQUIVALENT STATEMENTS OF A HILBERT-TYPE INTEGRAL INEQUALITY WITH THE RIEMANN-ZETA FUNCTION

Weiliang Wu¹,
Bicheng Yang^2, ,

1.
Department of Mathematics, Jiayin University, Jiayin, Guangdong 514015, China
2.
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China

Corresponding author: Email address:bcyang@gdei.edu.cn(B. Yang)

Abstract

Abstract

By using the way of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality in the whole plane with the internal variables and the best possible constant factor related to the Riemann-zeta function is proved. The operator expression and some particular cases are considered.
- Hilbert-type integral inequality /
- weight function /
- internal variable /
- equivalent statement /
- operator /
- Riemann-zeta function
MSC: 26D15, 31A10

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References

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