We study Sobolev estimates for solutions of the inhomogenous Cauchy–Riemann equations on annuli in \({\mathbb {C}}^n\), by constructing exact sequences relating the Dolbeault cohomology of the annulus with respect to Sobolev spaces of forms with those of the envelope and the hole. We also obtain solutions with prescribed support and estimates in Sobolev spaces using our method.

中文翻译：

---

$$ \ overline {\ partial} $$--问题的精确序列和估计

我们通过构造与环的Sobolev形式空间有关的环的Dolbeault同调性的精确序列，研究Sobolev估计，用于解决\（{{mathbb {C}} ^ n \）上环上非均匀Cauchy–Riemann方程的解。信封和孔。我们还使用我们的方法在Sobolev空间中获得具有规定支持和估计的解决方案。