Bounded operators on weak Hardy spaces and applications
type: Item
instance of: scholarly article
title: Bounded operators on weak Hardy spaces and applications
zbMATH Open document ID: 0914.42021
DOI: 10.1023/A:1006506911122
published in: Acta Mathematica Hungarica
publication date: 1999-03-14T00:00:00Z
review text: The author considers Vilenkin systems and martingales with respect to the sequence of \(\sigma\)-algebras generated by a Vilenkin system. A new concept of atoms, the so-called weak atom is introduced, and the martingales from the weak Hardy space \(wH_p\), \(0<p<\infty\), are decomposed into the sum of weak atoms. This atomic decomposition is used for some applications. Some sufficent conditions for a sublinear operator \(T\) to be bounded from \(wH_p\) to \(wL_p\) are given as well as a weak version of the Hardy-Littlewood inequality is obtained. Vilenkin-Fourier series are considered and by certain assumptions almost everywhere convergence of the Cesàro means of a function \(f\in L_1\) is proved.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 1261214
zbMATH Keywords: weak Hardy spaces
zbMATH Keywords: Vilenkin martingales
zbMATH Keywords: atomic decomposition
zbMATH Keywords: Vilenkin systems
zbMATH Keywords: Hardy-Littlewood inequality
zbMATH Keywords: Vilenkin-Fourier series
author: Ferenc Weisz
MaRDI profile type: Publication
full work available at URL: a:1006506911122
OpenAlex ID: W1838392141
description: scientific article; zbMATH DE number 1261214