Iterated commutators and derivatives of the levi form
Iterated commutators and derivatives of the levi form
复制标题
迭代换向器和列维形式的导数
DOI：
10.1007/bfb0097299
复制
发表时间：
1987
影响因子：
2.2
通讯作者：
J. D'Angelo
中科院分区：
文献类型：
--
作者：
J. D'Angelo
对于 3 维 CR 流形，结果很简单，不需要 3 伪凸假设。对于赝凸超曲面，结果可以从Bloom [lJ.这样的超曲面是维度为 5 的 CR 流形。对于某些特定的向量场（例如最小类型的向量场）也很容易验证这一点，但一般情况是开放的。在本文中我们获得了一些部分结果。首先，我们证明该猜想对于类型 4 的向量场成立。对于类型 2 的向量场来说，结果是微不足道的，并且在伪凸情况下，不可能存在类型 3 的向量场。其次，我们在类型（L，p）已知等于 N 的情况下给出 C（L，p）的估计。该估计的简化形式给出的结果* 部分由 NSF 拨款 MCS8l088l4（A04）支持，并且DMS850l008 和高等研究院。
For CRmanifolds of dimension 3, the result is trivial and does not require a 3 pseudoconvexity hypothesis. For pseudoconvex hypersurfaces in, the result can be derived from the work of Bloom [lJ. Such hypersurfaces are CRmanifolds of dimension 5. It is also easy to verify this for certain particular vector fields, such as a vector field of minimal type, but the general case is open. In this paper we obtain some partial results. First of all, we show that the conjecture holds for vector fields of type 4. The result is trivial for vector fields of type 2, and in the pseudoconvex case, there cannot be vector fields of type 3. Secondly, we give an estimate for C (L, p) in case type(L, p) is known to equal N A simplified form of this estimate gives the result that* Partially supported by the NSF Grants MCS8l088l4 (A04) and DMS850l008 and by The Institute for Advanced Study.