The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator

The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator

The authors prove that Marcinkiewicz integral operator is not only are bounded on Lp, for 1<P<∞, but also a bounded map from L1(Rn) to weak L1(Rn). Meanwhile, the BMOL-boundedness and (HL1,L1)-boundedness are also obtained. Finally, the Lp-boundedness and (L∞,BMOL)-boundedness for the commutat...

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Main Authors: Dongxiang Chen, Dan Zou
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2014/402713
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spelling doaj-715c6ad3d60f4fd594ba2f068aa420092020-11-25T00:31:52ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/402713402713The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its CommutatorDongxiang Chen0Dan Zou1Department of Mathematics, Jiangxi Normal University, Nanchang 330022, ChinaDepartment of Mathematics, Jiangxi Normal University, Nanchang 330022, ChinaThe authors prove that Marcinkiewicz integral operator is not only are bounded on Lp, for 1<P<∞, but also a bounded map from L1(Rn) to weak L1(Rn). Meanwhile, the BMOL-boundedness and (HL1,L1)-boundedness are also obtained. Finally, the Lp-boundedness and (L∞,BMOL)-boundedness for the commutator of Marcinkiewicz integral of schrödinger type are established.http://dx.doi.org/10.1155/2014/402713
collection DOAJ
language English
format Article
sources DOAJ
author Dongxiang Chen
Dan Zou
spellingShingle Dongxiang Chen
Dan Zou
The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator
Journal of Function Spaces
author_facet Dongxiang Chen
Dan Zou
author_sort Dongxiang Chen
title The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator
title_short The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator
title_full The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator
title_fullStr The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator
title_full_unstemmed The Boundedness of Marcinkiewicz Integral Associated with Schrödinger Operator and Its Commutator
title_sort boundedness of marcinkiewicz integral associated with schrödinger operator and its commutator
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2014-01-01
description The authors prove that Marcinkiewicz integral operator is not only are bounded on Lp, for 1<P<∞, but also a bounded map from L1(Rn) to weak L1(Rn). Meanwhile, the BMOL-boundedness and (HL1,L1)-boundedness are also obtained. Finally, the Lp-boundedness and (L∞,BMOL)-boundedness for the commutator of Marcinkiewicz integral of schrödinger type are established.
url http://dx.doi.org/10.1155/2014/402713
work_keys_str_mv AT dongxiangchen theboundednessofmarcinkiewiczintegralassociatedwithschrodingeroperatoranditscommutator
AT danzou theboundednessofmarcinkiewiczintegralassociatedwithschrodingeroperatoranditscommutator
AT dongxiangchen boundednessofmarcinkiewiczintegralassociatedwithschrodingeroperatoranditscommutator
AT danzou boundednessofmarcinkiewiczintegralassociatedwithschrodingeroperatoranditscommutator
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