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On Carleman's and Knopp's inequalities
Department of Mathematics, Uppsala University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematics and Statistics, University College of Gävle.
2002 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 117, no 1, p. 140-151Article in journal (Refereed) Published
Abstract [en]

A sharpened version of Carleman's inequality is proved. This result unifies and generalizes some recent results of this type. Also the “ordinary” sum that serves as the upper bound is replaced by the corresponding Cesaro sum. Moreover, a Carleman-type inequality with a more general measure is proved and this result may also be seen as a generalization of a continuous variant of Carleman's inequality, which is usually referred to as Knopp's inequality. A new elementary proof of (Carleman–)Knopp's inequality and a new inequality of Hardy–Knopp type is pointed out

Place, publisher, year, edition, pages
2002. Vol. 117, no 1, p. 140-151
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-6074DOI: 10.1006/jath.2002.3684Local ID: 44660670-64ca-11db-8cbe-000ea68e967bOAI: oai:DiVA.org:ltu-6074DiVA: diva2:978951
Note
Validerad; 2002; 20061026 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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