Year: 2023
Type: preprint
Abstract: In this paper, we first answer Chen-Zhang's problem on $p$-Bergman metric proposed in \cite{CZ22}. Second, we prove the off-diagonal p-Bergman kernel function $K_p(z,w)$ is Hölder continuous of order (1-$\varepsilon$) about the second component when $p>1$ for any $\varepsilon>0$, which improves the corresponding result of Chen-Zhang. Moreover, we prove the asymptotic behavior of the maximizer of $p$-Bergman kernel as $p\rightarrow 1^-$. Finally, we give a characterization of a class of holomorphic functions on $\mathbb{B}^1$ to be $L^p$-integrable.
Source: arXiv (Cornell University)
Author: Li, Yinji
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386614576