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Multidimensional Discrete Hilbert-Type Inequalities, Operators and Compositions

Abstract

Hilbert-type inequalities with their operators are important in analysis and its applications. In this paper by using the methods of weight coefficients and technique of real analysis, a multidimensional discrete Hilbert-type inequality with a best possible constant factor is given. The equivalent forms, two types of reverses, a more accurate inequality with parameters, as well as a strengthened version of Hardy-Hilbert’s inequality with Euler constant are obtained. We also consider the relating operators with the norms, some particular examples and the compositions of two discrete Hilbert-type operators in certain conditions.

Keywords

  • Half-discrete Hilbert-type Inequalities
  • Accurate Inequality
  • Euler Constant
  • Weight Coefficients
  • Constant Factor

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

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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Correspondence to Bicheng Yang .

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Dedicated to Professor Hari M. Srivastava

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Yang, B. (2014). Multidimensional Discrete Hilbert-Type Inequalities, Operators and Compositions. In: Milovanović, G., Rassias, M. (eds) Analytic Number Theory, Approximation Theory, and Special Functions. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0258-3_15

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