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Equivalent Statements of Hilbert-Type Integral Inequalities

  • Bicheng Yang
  • Michael Th. RassiasEmail author
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter, by the use of methods of real analysis and weight functions, we consider a few equivalent statements of Hilbert-type integral inequalities with a general nonhomogeneous kernel related to certain parameters. In the form of applications, a few equivalent statements of Hilbert-type integral inequalities with a general homogeneous kernel are deduced. Moreover, we also consider operator expressions, a few particular cases, and some examples related to the extended Hurwitz zeta function as applications.

References

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    Zhong, Y.Q.: Introduction to Complex Functions (Third Volume). Higher Education Press, Beijing (2003)Google Scholar
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    Wang, Z.X., Guo, D.R.: Introduction to Special Functions. Science Press, Beijing (1979)Google Scholar

Copyright information

© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsGuangdong University of EducationGuangzhouChina
  2. 2.Institute of MathematicsUniversity of ZurichZürichSwitzerland
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  4. 4.Institute for Advanced Study Program in Interdisciplinary StudiesPrincetonUSA

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