$L^p$ regularity of the Bergman projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$
| Autor: | Fu, Qian, Deng, Guan-Tie, Cao, Hui |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we investigate a class of domains $\Omega^{n+1}_k =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^k < |w| < 1\}$ for $k \in \mathbb{Z}^+$ which generalizes the Hartogs triangle. we first obtain the new explicit formulas for the Bergman kernel function on these domains and further give a range of $p$ values for which the $L^p$ boundedness of the Bergman projection holds. This range of $p$ is shown to be sharp. Comment: 16 pages, welcome to comment |
| Databáze: | arXiv |
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