Relating coefficients of expansion of a function to its norm
type: Item
instance of: scholarly article
title: Relating coefficients of expansion of a function to its norm
zbMATH Open document ID: 1348.42028
author: Z. Ditzian
published in: Journal of Mathematical Analysis and Applications
publication date: 2016-08-18T00:00:00Z
review text: For the expansion of a function by a complete weighted orthonormal system, the paper establishes estimates of the corresponding weighted \(L_p\)-norms of the function in terms of certain series involving the coefficients of the expansion. The proofs are obtained first for two special cases, which are the analogues of the Hausdorff-Young and the Hardy-Littlewood inequalities. Then the general results are proved via Stein's modification of the Riesz-Thorin interpolation theorem. It is shown that the results can be used for a variety of examples of orthogonal expansions.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 6618089
zbMATH Keywords: Hausdorff-Young, Hardy-Littlewood and Nikolskii inequalities
zbMATH Keywords: Christoffel functions
zbMATH Keywords: \(L_p\) norm
reviewed by: Aurelian Bejancu
MaRDI profile type: Publication
full work available at URL: j.jmaa.2016.07.002
OpenAlex ID: W2467864014
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DOI: 10.1016/J.JMAA.2016.07.002
description: scientific article; zbMATH DE number 6618089