On the $p$-Bergman kernel with respect to a functional $ξ$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917018038435840 |
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| author | Bao, Shijie Guan, Qi'an Sun, Xun |
| author_facet | Bao, Shijie Guan, Qi'an Sun, Xun |
| contents | In the present paper, we generalize the notion of the $p$-Bergman kernel and the $ξ$-Bergman kernel to the $p$-Bergman kernel with respect to a functional $ξ$, and establish some properties of the $p$-Bergman kernel with respect to $ξ$. We also study the relations between the $L^p$ versions of higher order Bergman kernels and $ξ$-Bergman kernels, and as applications we give the reproofs and generalizations of some previous results of Blocki and Zwonek about higher order Bergman kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $p$-Bergman kernel with respect to a functional $ξ$ Bao, Shijie Guan, Qi'an Sun, Xun Complex Variables 32A36, 32A70, 32D15, 32L05, 32U05 In the present paper, we generalize the notion of the $p$-Bergman kernel and the $ξ$-Bergman kernel to the $p$-Bergman kernel with respect to a functional $ξ$, and establish some properties of the $p$-Bergman kernel with respect to $ξ$. We also study the relations between the $L^p$ versions of higher order Bergman kernels and $ξ$-Bergman kernels, and as applications we give the reproofs and generalizations of some previous results of Blocki and Zwonek about higher order Bergman kernels. |
| title | On the $p$-Bergman kernel with respect to a functional $ξ$ |
| topic | Complex Variables 32A36, 32A70, 32D15, 32L05, 32U05 |
| url | https://arxiv.org/abs/2510.13144 |