论文标题
伯格曼内核的边界规律性在霍尔德空间
Boundary Regularity of Bergman Kernel in Hölder space
论文作者
论文摘要
令$ d $为$ \ mathbb {c}^n $中的严格pseudoconvex域。假设$ bd \ in c^{k+3+α} $，其中$ k $是一个非阴性整数，$ 0 <α\ leq 1 $，我们表明1）伯格曼内核$ b（\ cdot，w_0） \ in D $; 2）伯格曼对$ d $的投影是一个有限的操作员，从$ c^{k +β}（\ overline d）$到$ c^{k + \ \ \ \ \ {α，\fracβ{2} \}}}}（\ edline d）（\ edimline d）$。我们的结果既改进又概括了大肠杆菌的工作。
Let $D$ be a bounded strictly pseudoconvex domain in $\mathbb{C}^n$. Assuming $bD \in C^{k+3+α}$ where $k$ is a non-negative integer and $0 < α\leq 1$, we show that 1) the Bergman kernel $B(\cdot, w_0) \in C^{k+ \min\{α, \frac12 \} } (\overline D)$, for any $w_0 \in D$; 2) The Bergman projection on $D$ is a bounded operator from $C^{k+β}(\overline D)$ to $C^{k + \min \{ α, \fracβ{2} \}}(\overline D) $ for any $0 < β\leq 1$. Our results both improve and generalize the work of E. Ligocka.
