The weighted reproducing kernels of the Reinhardt domain
| Autor: | Fu, Qian, Deng, Guantie |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origin. As applications, we calculate the concrete forms of the Bergman kernels for some special weights on the Reinhardt domains $\mathbb{C}^n,$ $D_{n,m}:= \{(z, w)\in \mathbb{C}^n \times \mathbb{C}^m : \|w\|^2 <{e}^{-\mu_1\|z\|^{\mu_2}}\}$ and $V_{\eta}:=\{(z, z', w) \in \mathbb{C}^{n} \times \mathbb{C}^{m} \times \mathbb{C} : \sum_{j=1}^{n} e^{\eta_{j}|w|^{2}}|z_{j}|^{2}+\|z'\|^{2}<1\}$. Comment: 17 pages, any comments are welcome |
| Databáze: | arXiv |
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