On a Half-Discrete Hilbert-Type Inequality in the Whole Plane with the Kernel of Hyperbolic Secant Function Related to the Hurwitz Zeta Function

  • Michael Th. RassiasEmail author
  • Bicheng Yang
  • Andrei Raigorodskii


Using weight functions, we obtain a half-discrete Hilbert-type inequality in the whole plane with the kernel of hyperbolic secant function and multi-parameters. The constant factor related to the Hurwitz zeta function is proved to be the best possible. We also consider equivalent forms, two kinds of particular inequalities, the operator expressions and some reverses.


Half-discrete Hilbert-type inequality Weight function Equivalent form Operator expression Hurwitz zeta function 

2000 Mathematics Subject Classification

26D15 30A10 47A05 



B. Yang: This work is supported by the National Natural Science Foundation (No. 61772140), and Science and Technology Planning Project Item of Guangzhou City (No. 201707010229). I would like to express my gratitude for this support.


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Authors and Affiliations

  • Michael Th. Rassias
    • 1
    • 2
    • 3
    Email author
  • Bicheng Yang
    • 4
  • Andrei Raigorodskii
    • 2
    • 5
    • 6
    • 7
  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 EducationGuangzhou, GuangdongP. R. China
  5. 5.Moscow State UniversityMoscowRussia
  6. 6.Buryat State UniversityUlan-UdeRussia
  7. 7.Caucasus Mathematical CenterAdyghe State UniversityMaykopRussia

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