Half-Discrete Hilbert-Type Inequalities, Operators and Compositions

Bicheng Yang ()
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Bicheng Yang: Guangdong University of Education

A chapter in Handbook of Functional Equations, 2014, pp 459-534 from Springer

Abstract: Abstract In this chapter, using the methods of weight functions and technique of real analysis, a half-discrete Hilbert-type inequality with a homogeneous kernel and a best possible constant factor is provided. Some equivalent representations, two types of reverses, the operator expressions as well as some particular examples are obtained. Furthermore, we also consider some strengthened versions of half-discrete Hilbert’s inequality relating to Euler constant, the related inequalities and operators with the non-homogeneous kernel, and two kinds of compositions of two operators in certain conditions.

Keywords: Half-discrete Hilbert-type inequality; Weight function; Equivalent form; Hilbert-type operator; Composition (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_19

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DOI: 10.1007/978-1-4939-1246-9_19

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