Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes
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| Format: | Preprint |
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2025
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| _version_ | 1866915193726959616 |
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| author | Hong, Guixiang Lai, Xudong Wang, Liang |
| author_facet | Hong, Guixiang Lai, Xudong Wang, Liang |
| contents | In this paper, we establish a local smoothing estimate on two-dimensional quantum Euclidean space. This is the noncommutative analogue of the one due to Mockenhaupt$-$Seeger$-$Sogge \cite{MSS}. As an application and simultaneously one motivation, we obtain the noncommutative analogue of Bourgain's circular maximal theorem, resolving one problem after \cite{Hong}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_08832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes Hong, Guixiang Lai, Xudong Wang, Liang Functional Analysis 46L51, 42B20 In this paper, we establish a local smoothing estimate on two-dimensional quantum Euclidean space. This is the noncommutative analogue of the one due to Mockenhaupt$-$Seeger$-$Sogge \cite{MSS}. As an application and simultaneously one motivation, we obtain the noncommutative analogue of Bourgain's circular maximal theorem, resolving one problem after \cite{Hong}. |
| title | Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes |
| topic | Functional Analysis 46L51, 42B20 |
| url | https://arxiv.org/abs/2501.08832 |