论文标题
$ l^p $ bergman对hartogs Triangle概括的预测$ \ mathbb {c}^{n+1} $
$L^p$ regularity of the Bergman projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$
论文作者
论文摘要
在本文中，我们研究了一类域$ω^{n+1} _k = \ {（z，w）\ in \ mathbb {c}^n \ times \ times \ times \ mathbb {c}：| z | | | |^k <| w | <1 \} $ for $ k \ in \ athbb {z}^+$，概括了hartogs triangle。我们首先在这些域上获得了伯格曼内核功能的新的显式公式，并进一步提供了$ p $值的范围，伯格曼投影的$ l^p $界面所具有。 $ p $的范围显示出锋利的。
In this paper we investigate a class of domains $Ω^{n+1}_k =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^k < |w| < 1\}$ for $k \in \mathbb{Z}^+$ which generalizes the Hartogs triangle. we first obtain the new explicit formulas for the Bergman kernel function on these domains and further give a range of $p$ values for which the $L^p$ boundedness of the Bergman projection holds. This range of $p$ is shown to be sharp.
