Multidimensional Discrete Hilbert-Type Inequalities, Operators and Compositions

Bicheng Yang ()
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Bicheng Yang: Guangdong University of Education, Department of Mathematics

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 429-484 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_15

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DOI: 10.1007/978-1-4939-0258-3_15

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