The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group
In this article, we define a kind of truncated maximal function on the Heisenberg space by Mγcfx=sup0<r<γ1/mBx,r∫Bx,rfydy. The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, w...
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| Format: | Article |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/7612482 |
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| author | Xiang Li Xingsong Zhang |
| author_facet | Xiang Li Xingsong Zhang |
| author_sort | Xiang Li |
| collection | DOAJ |
| description | In this article, we define a kind of truncated maximal function on the Heisenberg space by Mγcfx=sup0<r<γ1/mBx,r∫Bx,rfydy. The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, when 1<p<∞, the Lp norm and central Morrey norm of truncated maximal function are equal to those of the Hardy-Littlewood maximal function. When p=1, we get the equivalence of weak norm L1⟶L1,∞ and Ṁ1,λ⟶ẆM1,λ. Those results are generalization of previous work on Euclid spaces. |
| format | Article |
| id | doaj-art-11184b5c59e14af2a8c8bed567302c9a |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-11184b5c59e14af2a8c8bed567302c9a2025-02-03T07:23:53ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/76124827612482The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg GroupXiang Li0Xingsong Zhang1School of Mathematics and Finance, Chuzhou University, Chuzhou, Anhui 239012, ChinaRDFZ Chaoyang School, Beijing 100028, ChinaIn this article, we define a kind of truncated maximal function on the Heisenberg space by Mγcfx=sup0<r<γ1/mBx,r∫Bx,rfydy. The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, when 1<p<∞, the Lp norm and central Morrey norm of truncated maximal function are equal to those of the Hardy-Littlewood maximal function. When p=1, we get the equivalence of weak norm L1⟶L1,∞ and Ṁ1,λ⟶ẆM1,λ. Those results are generalization of previous work on Euclid spaces.http://dx.doi.org/10.1155/2021/7612482 |
| spellingShingle | Xiang Li Xingsong Zhang The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group Journal of Function Spaces |
| title | The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group |
| title_full | The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group |
| title_fullStr | The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group |
| title_full_unstemmed | The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group |
| title_short | The Equivalence of Operator Norm between the Hardy-Littlewood Maximal Function and Truncated Maximal Function on the Heisenberg Group |
| title_sort | equivalence of operator norm between the hardy littlewood maximal function and truncated maximal function on the heisenberg group |
| url | http://dx.doi.org/10.1155/2021/7612482 |
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