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On an elementary approach to the fractional Hardy inequality
LuleƄ University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
2000 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 128, no 3, 727-734 p.Article in journal (Refereed) Published
Abstract [en]

Let be the usual Hardy operator, i.e., . We prove that the operator is bounded and has a bounded inverse on the weighted spaces for -1$" type="#_x005F_x0000_t75">and . Moreover, by using these inequalities we derive a somewhat generalized form of some well-known fractional Hardy type inequalities and also of a result due to Bennett-DeVore-Sharpley, where the usual Lorentz norm is replaced by an equivalent expression. Examples show that the restrictions in the theorems are essential.

Place, publisher, year, edition, pages
2000. Vol. 128, no 3, 727-734 p.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-7835DOI: 10.1090/S0002-9939-99-05420-9Local ID: 6419a300-a575-11db-9811-000ea68e967bOAI: oai:DiVA.org:ltu-7835DiVA: diva2:980725
Note
Validerad; 2000; 20070110 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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CiteExportLink to record
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