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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2507.15498 |
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| _version_ | 1866917063616888832 |
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| author | Cheng, Jiajun Fregoli, Reynold Guo, Beinuo |
| author_facet | Cheng, Jiajun Fregoli, Reynold Guo, Beinuo |
| contents | We generalize results of Jones and Olsen on multi-parameter moving ergodic averages to measure-preserving actions of $\mathbb R^d$ for $d\geq 1$. In particular, we give necessary and sufficient conditions for the pointwise convergence of averages over families of boxes in $\mathbb R^d$. As an application of our characterization, we show that averages along dilates of "locally flat" submanifolds in $\mathbb R^d$ do not necessarily converge point-wise for bounded measurable functions. This is closely related to the concept of submanifold-genericity recently introduced in \cite{BFK25}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-Dimensional Moving Averages and Submanifold Genericity Cheng, Jiajun Fregoli, Reynold Guo, Beinuo Dynamical Systems 37A25, 37A30, 28D05, 28D15 We generalize results of Jones and Olsen on multi-parameter moving ergodic averages to measure-preserving actions of $\mathbb R^d$ for $d\geq 1$. In particular, we give necessary and sufficient conditions for the pointwise convergence of averages over families of boxes in $\mathbb R^d$. As an application of our characterization, we show that averages along dilates of "locally flat" submanifolds in $\mathbb R^d$ do not necessarily converge point-wise for bounded measurable functions. This is closely related to the concept of submanifold-genericity recently introduced in \cite{BFK25}. |
| title | Higher-Dimensional Moving Averages and Submanifold Genericity |
| topic | Dynamical Systems 37A25, 37A30, 28D05, 28D15 |
| url | https://arxiv.org/abs/2507.15498 |