Abstract:We give examples of pseudoconvex domains of finite type in $\mathbb {C}^2$ where the Kohn algorithm for subelliptic estimates fails to yield an effective lower bound for the order of subellipticity in terms of the type. We show how to modify the algorithm to obtain an effective procedure to prove subellipticity on domains of finite type in $\mathbb {C}^2$ with real analytic boundary satisfying a condition slightly stronger than pseudoconvexity. We close with a generalization to higher dimensions.

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中文翻译：

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ℂ² 中的亚椭圆乘法器算法

摘要：我们在 $\mathbb {C}^2$ 中给出了有限类型的伪凸域的例子，其中用于亚椭圆估计的 Kohn 算法未能根据类型产生亚椭圆度阶数的有效下界。我们展示了如何修改算法以获得有效的程序来证明 $\mathbb {C}^2$ 中有限类型域的亚椭圆性，实解析边界满足比伪凸性稍强的条件。我们以对更高维度的概括结束。

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