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Multidimensional Hardy-type inequalities via convexity
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
University of Zagreb.
2008 (English)In: Bulletin of the Australian Mathematical Society, ISSN 0004-9727, E-ISSN 1755-1633, Vol. 77, no 2, p. 245-260Article in journal (Refereed) Published
Abstract [en]

Let an almost everywhere positive function Φ be convex for p>1 and p<0, concave for p∈(0,1), and such that Axp≤Φ(x) ≤Bxp holds on ℝ+ for some positive constants A≤B. In this paper we derive a class of general integral multidimensional Hardy-type inequalities with power weights, whose left-hand sides involve Φ (∫0x1⋯∫0xnf(t) dt) instead of [(∫0x1⋯∫0xnf(t) dt]p, while the corresponding right-hand sides remain as in the classical Hardy's inequality and have explicit constants in front of integrals. We also prove the related dual inequalities. The relations obtained are new even for the one-dimensional case and they unify and extend several inequalities of Hardy type known in the literature.

Place, publisher, year, edition, pages
2008. Vol. 77, no 2, p. 245-260
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-9528DOI: 10.1017/S0004972708000245ISI: 000257504100005Scopus ID: 2-s2.0-44949225983Local ID: 82e67dc0-737e-11dd-a60f-000ea68e967bOAI: oai:DiVA.org:ltu-9528DiVA, id: diva2:982466
Note
Validerad; 2008; 20080826 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Oguntuase, JamesPersson, Lars-Erik

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