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Some scales of equivalent weight characterizations of Hardy's inequality: the case q
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2007 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 2, 267-279 p.Article in journal (Refereed) Published
Abstract [en]

We consider the weighted Hardy inequality (∫0∞ (∫0x f(t)dt)q u(x)dx)1/q ≤ C(∫0∞ f p(x)v(x)dx)1/p for the case 0 < q < p < ∝, p > 1. The weights u(x) and v(x) for which this inequality holds for all f (x) ≥ 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanov conditions. In this paper, we show that these conditions are not unique and can be supplemented by some continuous scales of conditions and we prove their equivalence. The results for the dual operator which do not follow by duality when 0 < q < 1 are also given

Place, publisher, year, edition, pages
2007. Vol. 10, no 2, 267-279 p.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-10235Local ID: 90040fa0-57b3-11dc-a7ae-000ea68e967bOAI: oai:DiVA.org:ltu-10235DiVA: diva2:983175
Note
Validerad; 2007; 20070831 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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