$L^p$-boundedness of Berezin transforms on generalized Hartogs triangles
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918535249264640 |
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| author | Fu, Qian |
| author_facet | Fu, Qian |
| contents | Let $m,l\in\N$ be relatively prime and let \[ Ω_{m/l}^{n+1}=\bigl\{(z,w)\in\C^n\times\C:\ \norm{z}^{m}<\abs{w}^{l}<1\bigr\} \] be the rational generalized Hartogs triangle of exponent $m/l$ in $\C^{n+1}$. In this paper, we study the Berezin transform $\BB_{m/l,n}$ associated with the Bergman kernel of $Ω_{m/l}^{n+1}$, and prove that $\BB_{m/l,n}$ is bounded on $L^p(Ω_{m/l}^{n+1})$ if and only if $p>m+nl$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02364 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L^p$-boundedness of Berezin transforms on generalized Hartogs triangles Fu, Qian Complex Variables 32A36, 47B35, 47G30 Let $m,l\in\N$ be relatively prime and let \[ Ω_{m/l}^{n+1}=\bigl\{(z,w)\in\C^n\times\C:\ \norm{z}^{m}<\abs{w}^{l}<1\bigr\} \] be the rational generalized Hartogs triangle of exponent $m/l$ in $\C^{n+1}$. In this paper, we study the Berezin transform $\BB_{m/l,n}$ associated with the Bergman kernel of $Ω_{m/l}^{n+1}$, and prove that $\BB_{m/l,n}$ is bounded on $L^p(Ω_{m/l}^{n+1})$ if and only if $p>m+nl$. |
| title | $L^p$-boundedness of Berezin transforms on generalized Hartogs triangles |
| topic | Complex Variables 32A36, 47B35, 47G30 |
| url | https://arxiv.org/abs/2606.02364 |