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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/6759632 |
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| _version_ | 1832554515094568960 |
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| author | Feng Liu Lei Xu |
| author_facet | Feng Liu Lei Xu |
| author_sort | Feng Liu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ab7737d3698a4b9e9ffc704cf9274a7f |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ab7737d3698a4b9e9ffc704cf9274a7f2025-02-03T05:51:18ZengWileyJournal 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 |
| spellingShingle | Feng Liu Lei Xu A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function Journal of Function Spaces |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2018/6759632 |
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