Hardy-Littlewood type inequalities for Vilenkin-Fourier coefficients
type: Item
instance of: scholarly article
title: Hardy-Littlewood type inequalities for Vilenkin-Fourier coefficients
zbMATH Open document ID: 0913.42020
DOI: 10.1007/BF02771078
published in: Analysis Mathematica
publication date: 1999-03-14T00:00:00Z
review text: The Hardy type inequality \[ \left(\sum_{k=3D1}^{\infty}\frac{| \widehat f(k)| ^p}{k^{2-p}}\right) \leq C_p \| f\| _{H^p_{**}} \quad (1/2 < p\leq 2) \tag{\(\ast\)} \] is proved for functions \(f\) belonging to the Hardy space \(H^p_{**}(G_m)\) defined by means of a maximal function. The authors extend (\(\ast\)) for \(2<p<\infty\) when the Vilenkin-Fourier coefficients of \(f\) are \(\lambda\)-blockwise monotone. They show that under some conditions on the Vilenkin system (in particular, for some unbounded type, too) a converse version of (\(\ast\)) holds also for all \(p>0\) provided that the Vilenkin-Fourier coefficients of \(f\) are monotone.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 43A75
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1261156
zbMATH Keywords: Vilenkin system of unbounded type
zbMATH Keywords: Hardy spaces
zbMATH Keywords: Hardy type inequality
zbMATH Keywords: Vilenkin-Fourier coefficients
author: Péter L. Simon
author: Ferenc Weisz
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02771078
OpenAlex ID: W2316552537
description: scientific article; zbMATH DE number 1261156