Atomic decompositions of Lorentz martingale spaces and applications

Atomic decompositions of Lorentz martingale spaces and applications

In the paper we present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalitie...

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Main Authors: Jiao Yong, Peng Lihua, Liu Peide
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2009/465079
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spelling doaj-b83b969e973a4c28923c99e76c6533da2020-11-24T21:43:48ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022009-01-017215316610.1155/2009/465079Atomic decompositions of Lorentz martingale spaces and applicationsJiao Yong0Peng Lihua1Liu Peide2School of Mathematical Science and Computing Technology, Central South University, Chang Sha 410081, ChinaSchool of Mathematical Science and Computing Technology, Central South University, Chang Sha 410081, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaIn the paper we present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalities on Lorentz martingale spaces. Finally we discuss the restricted weak-type interpolation, and prove the classical Marcinkiewicz interpolation theorem in the martingale setting.http://dx.doi.org/10.1155/2009/465079
collection DOAJ
language English
format Article
sources DOAJ
author Jiao Yong
Peng Lihua
Liu Peide
spellingShingle Jiao Yong
Peng Lihua
Liu Peide
Atomic decompositions of Lorentz martingale spaces and applications
Journal of Function Spaces and Applications
author_facet Jiao Yong
Peng Lihua
Liu Peide
author_sort Jiao Yong
title Atomic decompositions of Lorentz martingale spaces and applications
title_short Atomic decompositions of Lorentz martingale spaces and applications
title_full Atomic decompositions of Lorentz martingale spaces and applications
title_fullStr Atomic decompositions of Lorentz martingale spaces and applications
title_full_unstemmed Atomic decompositions of Lorentz martingale spaces and applications
title_sort atomic decompositions of lorentz martingale spaces and applications
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
publishDate 2009-01-01
description In the paper we present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalities on Lorentz martingale spaces. Finally we discuss the restricted weak-type interpolation, and prove the classical Marcinkiewicz interpolation theorem in the martingale setting.
url http://dx.doi.org/10.1155/2009/465079
work_keys_str_mv AT jiaoyong atomicdecompositionsoflorentzmartingalespacesandapplications
AT penglihua atomicdecompositionsoflorentzmartingalespacesandapplications
AT liupeide atomicdecompositionsoflorentzmartingalespacesandapplications
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