论文标题
Hölder估计$ \ bar \ partial $问题的$（p，q）$表格在产品域中
Hölder estimates for the $\bar\partial$ problem for $(p,q)$ forms on product domains
论文作者
论文摘要
本文的目的是研究Hölder估计$ \ bar \ partial $问题的$（p，q）$ y th in Center Planar域产品的表格。如Stein和Kerzman的示例所示，在$ \ Mathbb C^n（N \ ge 2）$中，$ \ bar \ partial $问题的解决方案在HölderSpaces中无法获得规律性。 Making use of an integral representation of Nijenhuis and Woolf, we show that given a $\bar\partial$-closed $(p,q)$ form with $C^{k,α}$ components, $0\le p\le n, 1\le q\le n$, $k\in \mathbb Z^+\cup \{0\}, 0<α\le 1 $，对于任何$ 0 <α'<α$，$ c^{k，α'} $解决方案，以及所需的Hölder估计。
The purpose of this paper is to study Hölder estimates for the $\bar\partial$ problem for $(p,q)$ forms on products of general planar domains. As indicated by an example of Stein and Kerzman, solutions to the $\bar\partial$ problem on product domains in $\mathbb C^n (n\ge 2)$ does not gain regularity in Hölder spaces. Making use of an integral representation of Nijenhuis and Woolf, we show that given a $\bar\partial$-closed $(p,q)$ form with $C^{k,α}$ components, $0\le p\le n, 1\le q\le n$, $k\in \mathbb Z^+\cup \{0\}, 0<α\le 1$, there is a $C^{k, α'}$ solution to the $\bar\partial$ problem on product domains for any $0<α'<α$ with the desired Hölder estimate.
