$L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866913916952510464 |
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| author | Wang, Xing Xu, Xiangjin Zhang, Cheng |
| author_facet | Wang, Xing Xu, Xiangjin Zhang, Cheng |
| contents | Marzo and Ortega-Cerdà gave geometric characterizations for $L^p$-Logvinenko-Sereda sets on the standard sphere for all $1\le p<\infty$. Later, Ortega-Cerdà and Pridhnani further investigated $L^2$-Logvinenko-Sereda sets and $L^2$-Carleson measures on compact manifolds without boundary. In this paper, we characterize $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds with or without boundary for all $1<p<\infty$. Furthermore, we investigate $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures for eigenfunctions on compact manifolds without boundary, and we completely characterize them on the standard sphere $S^m$ for $p > \frac{2m}{m-1}$. For the range $p < \frac{2m}{m-1}$, we conjecture that $L^p$-Logvinenko-Sereda sets for eigenfunctions on the standard sphere $S^m$ are characterized by the tubular geometric control condition and we provide some evidence. These results provide new progress on an open problem raised by Ortega-Cerdà and Pridhnani. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_22759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds Wang, Xing Xu, Xiangjin Zhang, Cheng Analysis of PDEs Classical Analysis and ODEs Spectral Theory 35P99, 58C35, 58C40 Marzo and Ortega-Cerdà gave geometric characterizations for $L^p$-Logvinenko-Sereda sets on the standard sphere for all $1\le p<\infty$. Later, Ortega-Cerdà and Pridhnani further investigated $L^2$-Logvinenko-Sereda sets and $L^2$-Carleson measures on compact manifolds without boundary. In this paper, we characterize $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds with or without boundary for all $1<p<\infty$. Furthermore, we investigate $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures for eigenfunctions on compact manifolds without boundary, and we completely characterize them on the standard sphere $S^m$ for $p > \frac{2m}{m-1}$. For the range $p < \frac{2m}{m-1}$, we conjecture that $L^p$-Logvinenko-Sereda sets for eigenfunctions on the standard sphere $S^m$ are characterized by the tubular geometric control condition and we provide some evidence. These results provide new progress on an open problem raised by Ortega-Cerdà and Pridhnani. |
| title | $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Spectral Theory 35P99, 58C35, 58C40 |
| url | https://arxiv.org/abs/2506.22759 |