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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |