Harmonic Bergman spaces on locally finite trees
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909602607529984 |
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| author | Ottazzi, Alessandro Santagati, Federico |
| author_facet | Ottazzi, Alessandro Santagati, Federico |
| contents | We define the harmonic Bergman space on locally finite trees with respect to a suitable probabilistic Laplacian and a class of weighted flow measures. We characterise the corresponding Bergman projection and prove that it is bounded on $L^p$ for every $p>1$, and of weak type $(1,1)$. We also prove necessary and sufficient conditions for the $L^p$-boundedness of the extension of a class of Toeplitz-type operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic Bergman spaces on locally finite trees Ottazzi, Alessandro Santagati, Federico Functional Analysis Complex Variables We define the harmonic Bergman space on locally finite trees with respect to a suitable probabilistic Laplacian and a class of weighted flow measures. We characterise the corresponding Bergman projection and prove that it is bounded on $L^p$ for every $p>1$, and of weak type $(1,1)$. We also prove necessary and sufficient conditions for the $L^p$-boundedness of the extension of a class of Toeplitz-type operators. |
| title | Harmonic Bergman spaces on locally finite trees |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2505.03479 |