On several problems in p-Bergman theory

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-$\epsilon$) about the second component when $p>1$ for any $\epsilon >0$, which improves the corresponding result of Chen-Zhang. Moreover, we prove the asymptotic behavior of the maximizer of $p$-Bergman kernel as $p\to 1^{-}$. Finally, we give a characterization of a class of holomorphic functions on ${\mathbb{B}}^1$ to be $L^p$-integrable.

10 pages