论文标题
$ \ bar \ partial $ sobolev的规律性在产品域上
Sobolev regularity of the canonical solutions to $\bar\partial$ on product domains
论文作者
论文摘要
令$ω$为$ \ Mathbb c^n，n \ ge 2 $中的产品域，每个切片都有光滑的边界。我们观察到，$ω$上的$ \ bar \ partial $方程的规范解决方案操作员以$ w^{k，p}（ω）$，$ k \ in \ mathbb z^+，1 <p <\ infty $进行限制。鉴于Kerzman型示例，这种Sobolev的规律性很清晰。
Let $Ω$ be a product domain in $\mathbb C^n, n\ge 2$, where each slice has smooth boundary. We observe that the canonical solution operator for the $\bar\partial$ equation on $Ω$ is bounded in $W^{k,p}(Ω)$, $k\in \mathbb Z^+, 1<p<\infty$. This Sobolev regularity is sharp in view of Kerzman-type examples.
