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On a Hilbert-Type Integral Inequality in the Whole Plane Related to the Extended Riemann Zeta Function

  • Michael Th. Rassias
  • Bicheng Yang
Article
  • 26 Downloads

Abstract

In the present paper, a few equivalent conditions of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The best possible constant factor is related to the extended Riemann zeta function. In the form of applications, a few equivalent conditions of a Hilbert-type integral inequality with the homogeneous kernel in the whole plane are deduced. We also consider the operator expressions and a few particular cases.

Keywords

Hilbert-type integral inequality Kernel Weight function Equivalent form Operator Norm 

Mathematics Subject Classification

26D15 47A07 65B10 

Notes

Acknowledgements

M. Th. Rassias: I would like to express my gratitude to the J. S. Latsis Foundation for their financial support provided under the auspices of my current “Latsis Foundation Senior Fellowship” position. B. Yang: This work is supported by the National Natural Science Foundation (Nos. 61370186, 61640222), and Appropriative Researching Fund for Professors and Doctors, Guangdong University of Education (No. 2015ARF25). I feel grateful for this help.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of ZurichZurichSwitzerland
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Institute for Advanced Study, Program in Interdisciplinary StudiesPrincetonUSA
  4. 4.Department of MathematicsGuangdong University of EducationGuangzhouPeople’s Republic of China

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