Hilbert-Type Inequalities Including Some Operators, the Best Possible Constants and Applications: A Survey

Vandanjav Adiyasuren (), Tserendorj Batbold () and Mario Krnić ()
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Vandanjav Adiyasuren: National University of Mongolia
Tserendorj Batbold: National University of Mongolia
Mario Krnić: University of Zagreb

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 17-52 from Springer

Abstract: Abstract The present work is a review article about some recent results dealing with Hilbert-type inequalities including certain operators in both integral and discrete case. A particular emphasis is given to inequalities including classical means operators. The constants appearing in all discussed inequalities are the best possible. For an illustration, some proofs are given, as well as some applications.

Keywords: Hilbert inequality; Hilbert-type inequality; Hardy inequality; Knopp inequality; Carleman inequality; The best possible constant; Mean operator; Primary 26D10; 26D15; Secondary 40A05; 33B15 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_2

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DOI: 10.1007/978-3-319-06554-0_2

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