On Carleman and Knopp's inequalities

Authors:
Sten Kaijser;Lars-Erik Persson;Anders Öberg
Affiliations:
Department of Mathematics, Uppsala University, P.O. Box 480, Uppsala, Sweden;Department of Mathematics, Luleå University of Technology, Luleå, Sweden;Department of Mathematics and Statistics, University College of Gävle, Gävle, Sweden
Venue:
Journal of Approximation Theory
Year:
2002

Citing 2
Cited 2

Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions

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Abstract

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.