Lacunary spherical maximal operators on hyperbolic spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916635096383488 |
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| author | Wang, Yunxiang Zhang, Hong-Wei |
| author_facet | Wang, Yunxiang Zhang, Hong-Wei |
| contents | We prove that the lacunary spherical maximal operator, defined on the $n$-dimensional real hyperbolic space, is bounded on $L^p(\mathbb{H}^n)$ for all $n\ge2$ and $1<p\le\infty$. In particular, the lacunary set is significantly larger than its Euclidean counterpart, reflecting the influence of the geometry at infinity of the hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lacunary spherical maximal operators on hyperbolic spaces Wang, Yunxiang Zhang, Hong-Wei Classical Analysis and ODEs 42B25, 43A85, 22E30, 43A90 We prove that the lacunary spherical maximal operator, defined on the $n$-dimensional real hyperbolic space, is bounded on $L^p(\mathbb{H}^n)$ for all $n\ge2$ and $1<p\le\infty$. In particular, the lacunary set is significantly larger than its Euclidean counterpart, reflecting the influence of the geometry at infinity of the hyperbolic space. |
| title | Lacunary spherical maximal operators on hyperbolic spaces |
| topic | Classical Analysis and ODEs 42B25, 43A85, 22E30, 43A90 |
| url | https://arxiv.org/abs/2502.20739 |