On inequalities of Bohr and Bernstein
type: Item
instance of: scholarly article
title: On inequalities of Bohr and Bernstein
zbMATH Open document ID: 1007.26011
DOI: 10.1155/S1025583402000176
author: Ha Huy Bang
published in: Journal of Inequalities and Applications
publication date: 2003-03-17T00:00:00Z
review text: The author proves inequalities of Bohr-Favard and Bernstein for \(N_\Phi\)-spaces generated by concave functions \(\Phi\). Among others he proves: Let \(f\) and its generalized derivative \(f^{(n)}\) be in \(N_\Phi(\mathbb{R})\) and \(\sup\widehat f\cap(- \sigma,\sigma)= \emptyset\). Then \(f^{(k)}\in N_\Phi(\mathbb{R})\) for all \(0< k< n\) and \[ \|f\|_{N_\Phi}\leq \sigma^{- n}K_n\|f^{(n)}\|_{N_\Phi}, \] where \(\widehat f\) is the Fourier transform of \(f\) and \(K_n\) is the \(n\)th Favard constant. An analogous theorem is proved on the torus, and some further pleasant results can be found in the paper.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26B35
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1820047
zbMATH Keywords: inequalities of Bohr-Favard and Bernstein
zbMATH Keywords: Fourier transform
zbMATH Keywords: Favard constant
reviewed by: László Leindler
MaRDI profile type: Publication
full work available at URL: s1025583402000176
OpenAlex ID: W1971124386
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description: scientific article; zbMATH DE number 1820047