ON A NEW HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE WITH THE GENERAL HOMOGENEOUS KERNEL

Bicheng Yang; Yanru Zhong; Aizhen Wang

doi:10.11948/20210039

2021 Volume 11 Issue 5

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Bicheng Yang, Yanru Zhong, Aizhen Wang. ON A NEW HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE WITH THE GENERAL HOMOGENEOUS KERNEL[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2583-2600. doi: 10.11948/20210039

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Bicheng Yang, Yanru Zhong, Aizhen Wang. ON A NEW HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE WITH THE GENERAL HOMOGENEOUS KERNEL[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2583-2600. doi: 10.11948/20210039

ON A NEW HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE WITH THE GENERAL HOMOGENEOUS KERNEL

1.
Department 0f Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China
2.
School of Computer Science and Information Security, Guilin University ofElectronic Technology, Guilin, Guangxi 541004, China

Corresponding author: Email: 18577399236@163.com(Y. Zhong)
Fund Project: The authors were supported by National Natural Science Foundation of China (62033001) and Characteristic Innovation Project of Guangdong Provincial Colleges and Universities in 2020 (2020KTSCX088)

Abstract

Abstract

By means of the weight coefficients and the idea of introducing parameters, a new discrete Hilbert -type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of Hardy-Hilbert's inequality. The equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered.
- Weight coefficient /
- Hilbert-type inequality /
- equivalent form /
- equivalent statement /
- parameter /
- operator expression
MSC: 26D15

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References

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