On Carleman's and Knopp's inequalities

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 p...

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Bibliographic Details
Published in:Journal of approximation theory 2002, Vol.117 (1), p.140
Main Authors: Kaijser, Sten, Persson, Lars-Erik, Öberg, Anders
Format: Article
Language:English
Subjects:
Matematik
Mathematics
Online Access:Get full text
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Summary: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
ISSN:0021-9045
1096-0430
DOI:10.1006/jath.2002.3684