Martingale Hardy spaces, BMO and VMO spaces with nonlinearly ordered stochastic basis
type: Item
instance of: scholarly article
title: Martingale Hardy spaces, BMO and VMO spaces with nonlinearly ordered stochastic basis
zbMATH Open document ID: 0708.60039
DOI: 10.1007/BF01906086
published in: Analysis Mathematica
publication date: 1990-01-01T00:00:00Z
review text: Some duality results of martingale theory are generalized in the case when the stochastic basis is nonlinearly ordered. The concepts of \(\infty\)-atom and atomic Hardy space are introduced. Duality between atomic Hardy, BMO and VMO spaces are proved. The analogue of the classical Hardy inequality is given for Walsh-Fourier coefficients of functions belonging to the two-dimensional dyadic Hardy space. Some of these theorems are generalized for q-atoms in another paper of the author titled ``Atomic Hardy spaces'' (to appear in the same journal).
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 60G48
zbMATH DE Number: 4163829
zbMATH Keywords: BMO and VMO spaces
zbMATH Keywords: Hardy inequality
zbMATH Keywords: duality results of martingale theory
zbMATH Keywords: Walsh-Fourier coefficients
zbMATH Keywords: two-dimensional dyadic Hardy space
author: Ferenc Weisz
reviewed by: Ferenc Weisz
MaRDI profile type: Publication
cites work: Distribution function inequalities for martingales
cites work: Extensions of Hardy spaces and their use in analysis
cites work: \(H^p\) spaces of several variables
cites work: Q4771939
cites work: Dyadic martingale Hardy and VMO spaces on the plane
full work available at URL: https://doi.org/10.1007/bf01906086
OpenAlex ID: W1755506106
description: scientific article; zbMATH DE number 4163829