On Two Kinds of the Hardy-Type Integral Inequalities in the Whole Plane with the Equivalent Forms

Bicheng Yang (), Dorin Andrica (), Ovidiu Bagdasar () and Michael Th. Rassias ()
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Bicheng Yang: Guangdong University of Education
Dorin Andrica: Babeş-Bolyai University
Ovidiu Bagdasar: University of Derby
Michael Th. Rassias: Hellenic Military Academy

A chapter in Mathematical Analysis in Interdisciplinary Research, 2021, pp 1025-1048 from Springer

Abstract: Abstract By the use of weight functions, a few equivalent conditions of two kinds of Hardy-type integral inequalities with multi-parameters in the whole plane are obtained. The constant factors related to the extended Riemann-zeta function are proved to be the best possible. Applying our results, we deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities in the whole plane and some particular cases.

Keywords: Hardy-type integral inequality; Weight function; Equivalent form; Parameter; Riemann-zeta function; Best constants; 26D15; 65B10 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84721-0_39

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DOI: 10.1007/978-3-030-84721-0_39

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