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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23047 |
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| _version_ | 1866913568061915136 |
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| author | Conde-Alonso, José M. De Mari, Filippo Monti, Matteo Rizzo, Elena Vallarino, Maria |
| author_facet | Conde-Alonso, José M. De Mari, Filippo Monti, Matteo Rizzo, Elena Vallarino, Maria |
| contents | We prove endpoint and sparse-like bounds for Bergman projectors on nonhomogeneous, radial trees $X$ that model manifolds with possibly unbounded geometry. The natural Bergman measures on $X$ may fail to be doubling, and even locally doubling, with respect to the right metric in our setting. Weighted consequences of our sparse domination results are also considered, and are in line with the known results in the disk. Our endpoint results are partly a consequence of a new Calderón-Zygmund theory for discrete, non-locally doubling metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23047 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Endpoint estimates and sparse domination in nonhomogeneous trees Conde-Alonso, José M. De Mari, Filippo Monti, Matteo Rizzo, Elena Vallarino, Maria Classical Analysis and ODEs Complex Variables 30H20, 32A25, 42B20, 39A12 We prove endpoint and sparse-like bounds for Bergman projectors on nonhomogeneous, radial trees $X$ that model manifolds with possibly unbounded geometry. The natural Bergman measures on $X$ may fail to be doubling, and even locally doubling, with respect to the right metric in our setting. Weighted consequences of our sparse domination results are also considered, and are in line with the known results in the disk. Our endpoint results are partly a consequence of a new Calderón-Zygmund theory for discrete, non-locally doubling metric spaces. |
| title | Endpoint estimates and sparse domination in nonhomogeneous trees |
| topic | Classical Analysis and ODEs Complex Variables 30H20, 32A25, 42B20, 39A12 |
| url | https://arxiv.org/abs/2410.23047 |