A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function

A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function

We investigate the regularity properties of the two-dimensional one-sided Hardy-Littlewood maximal operator. We point out that the above operator is bounded and continuous on the Sobolev spaces Ws,p(R2) for 0≤s≤1 and 1<p<∞. More importantly, we establish the sharp boundedness and continuity fo...

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Main Authors: Feng Liu, Lei Xu
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/6759632
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spelling doaj-ab7737d3698a4b9e9ffc704cf9274a7f2020-11-25T00:19:44ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/67596326759632A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal FunctionFeng Liu0Lei Xu1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, ChinaWe investigate the regularity properties of the two-dimensional one-sided Hardy-Littlewood maximal operator. We point out that the above operator is bounded and continuous on the Sobolev spaces Ws,p(R2) for 0≤s≤1 and 1<p<∞. More importantly, we establish the sharp boundedness and continuity for the discrete two-dimensional one-sided Hardy-Littlewood maximal operator from l1(Z2) to BV(Z2). Here BV(Z2) denotes the set of all functions of bounded variation on Z2.http://dx.doi.org/10.1155/2018/6759632
collection DOAJ
language English
format Article
sources DOAJ
author Feng Liu
Lei Xu
spellingShingle Feng Liu
Lei Xu
A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function
Journal of Function Spaces
author_facet Feng Liu
Lei Xu
author_sort Feng Liu
title A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function
title_short A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function
title_full A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function
title_fullStr A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function
title_full_unstemmed A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function
title_sort note on the regularity of the two-dimensional one-sided hardy-littlewood maximal function
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2018-01-01
description We investigate the regularity properties of the two-dimensional one-sided Hardy-Littlewood maximal operator. We point out that the above operator is bounded and continuous on the Sobolev spaces Ws,p(R2) for 0≤s≤1 and 1<p<∞. More importantly, we establish the sharp boundedness and continuity for the discrete two-dimensional one-sided Hardy-Littlewood maximal operator from l1(Z2) to BV(Z2). Here BV(Z2) denotes the set of all functions of bounded variation on Z2.
url http://dx.doi.org/10.1155/2018/6759632
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AT fengliu noteontheregularityofthetwodimensionalonesidedhardylittlewoodmaximalfunction
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