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arXiv · 2510.13144

On the $p$-Bergman kernel with respect to a functional $\xi$

Shijie Bao·Qi'an Guan·Xun Sun
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Abstract

In the present paper, we generalize the notion of the $p$-Bergman kernel and the $\xi$-Bergman kernel to the $p$-Bergman kernel with respect to a functional $\xi$, and establish some properties of the $p$-Bergman kernel with respect to $\xi$. We also study the relations between the $L^p$ versions of higher order Bergman kernels and $\xi$-Bergman kernels, and as applications we give the reproofs and generalizations of some previous results of Blocki and Zwonek about higher order Bergman kernels.

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Shijie Bao, Qi'an Guan, Xun Sun. 2025-10-15. On the $p$-Bergman kernel with respect to a functional $\xi$. https://arxiv.org/abs/2510.13144

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