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A Multidimensional Hilbert-Type Integral Inequality Related to the Riemann Zeta Function

  • Michael Th. RassiasEmail author
  • Bicheng Yang
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 91)

Abstract

In this chapter, using methods of weight functions and techniques of real analysis, we provide a multidimensional Hilbert-type integral inequality with a homogeneous kernel of degree 0 as well as a best possible constant factor related to the Riemann zeta function. Some equivalent representations and certain reverses are obtained. Furthermore, we also consider operator expressions with the norm and some particular results.

Keywords

Hilbert-type integral inequality Hilbert-type integral operator Riemann zeta function Gamma function Weight function 

Notes

Acknowledgements

The authors wish to express their thanks to Professors Tserendorj Batbold, Mario Krnic, and Jichang Kuang for their careful reading of the manuscript and for their valuable suggestions.

M. Th. Rassias: This work is supported by the Greek State Scholarship Foundation (IKY).

B. Yang: This work is supported by 2012 Knowledge Construction Special Foundation Item of Guangdong Institution of Higher Learning College and University (No. 2012KJCX0079).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsETH-ZentrumZurichSwitzerland
  2. 2.Department of MathematicsGuangdong University of EducationGuangzhouP. R. China

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