CR向量丛问题II的正则性
Regularity for the CR vector bundle problem II
摘要：
我们得到了$Pϕ$的一个$\mathcal C^{k+\yt}$ Hölder估计，其中$P$是$\mathbf C^{n}$中强伪凸实超曲面$M$上的$\bar\partial_b$的Henkin局部同伦公式中的两个解算子之一，$ϕ$是$M$上的类$\mathcal C^{k}$的$(0,q)$ -形式，$k\geq0$是整数.当$ϕ$为$\mathcal C^{a}$类且$a\geq0$为实数时，我们还得到了$Pϕ$的$\mathcal C^{a}$估计.这些估计要求$M$分别属于$\mathcal C^{k+{5/2}}$类或$\mathcal C^{a+2}$类。这些估计中出现的常数的明确界限也大大改善了以前已知的结果。这些估计，然后应用到CR向量丛的可积性问题，以获得改进的正则性。他们也构成了一个主要成分，在即将进行的工作的作者对当地的CR嵌入问题。
英文摘要：
We derive a $\mathcal C^{k+\yt}$ Hölder estimate for $Pϕ$, where $P$ is either of the two solution operators in Henkin's local homotopy formula for $\bar\partial_b$ on a strongly pseudoconvex real hypersurface $M$ in $\mathbf C^{n}$, $ϕ$ is a $(0,q)$-form of class $\mathcal C^{k}$ on $M$, and $k\geq0$ is an integer. We also derive a $\mathcal C^{a}$ estimate for $Pϕ$, when $ϕ$ is of class $\mathcal C^{a}$ and $a\geq0$ is a real number. These estimates require that $M$ be of class $\mathcal C^{k+{5/2}}$, or $\mathcal C^{a+2}$, respectively. The explicit bounds for the constants occurring in these estimates also considerably improve previously known such results. These estimates are then applied to the integrability problem for CR vector bundles to gain improved regularity. They also constitute a major ingredient in a forthcoming work of the authors on the local CR embedding problem.
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