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.
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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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Rassias, M.T., Yang, B. (2014). A Multidimensional Hilbert-Type Integral Inequality Related to the Riemann Zeta Function. In: Daras, N. (eds) Applications of Mathematics and Informatics in Science and Engineering. Springer Optimization and Its Applications, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-04720-1_26
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DOI: https://doi.org/10.1007/978-3-319-04720-1_26
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