Wiener's positive Fourier coefficients theorem in variants of \(L^p\) spaces
type: Item
instance of: scholarly article
title: Wiener's positive Fourier coefficients theorem in variants of \(L^p\) spaces
zbMATH Open document ID: 1204.42012
author: J. Martínez
published in: Michigan Mathematical Journal
publication date: 2010-06-17T00:00:00Z
review text: The authors consider the following classes of functions: the space \(L^p({\mathbb T)}\); the class of functions \(f\) with nonnegative Fourier coefficients such that \(|f|^p\) is integrable in a neighbourhood of \(0\); the space of functions whose Fourier coefficients belong to \(\ell^{p'}\); the space of functions \(f\) whose Fourier coefficients \(\{c_n\}\) satisfy \(\sum|c_n|\cdot|n|^{p-2}<\infty\); and the mixed norm spaces \(\ell^{p',2}\), \(1<p<2\). Various relationships between these classes are described.
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 42A32
Mathematics Subject Classification ID: 42A16
Mathematics Subject Classification ID: 42A55
zbMATH DE Number: 5723343
zbMATH Keywords: \(L^p\) spaces
zbMATH Keywords: Fourier coefficients
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1272376029
OpenAlex ID: W2083442917
cites work: Shorter Notes: Fourier Series with Positive Coefficients
cites work: Periodic Entire Functions
cites work: An extension of the Hausdorff-Young theorem
cites work: MAJORANT PROBLEMS FOR FOURIER COEFFICIENTS
cites work: Taylor coefficients of functions in Fock spaces
cites work: A Problem of Wiener and the Failure of a Principle for Fourier Series with positive Coefficients
DOI: 10.1307/MMJ/1272376029
description: scientific article; zbMATH DE number 5723343