Extension of holomorphic L 2-functions with weighted growth conditions
Extension of holomorphic L 2-functions with weighted growth conditions
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DOI：
10.1017/s0027763000004037
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发表时间：
1992-06
影响因子：
0.8
通讯作者：
K. Diederich;G. Herbort
中科院分区：
文献类型：
--
作者：
K. Diederich;G. Herbort
本文对如下问题作出了新的贡献：设Ω⊂⊂Cn是具有C∞光滑边界的有界伪凸域，Q∈∂Ω是不动点，H是k维仿射复平面，使得Q∈H和H在Q处横交∂Ω.设U是Q的一个适当小的邻域，r表示U上∞的一个CΩ定义函数，在此条件下，在Q附近的∂Ω上有可能找到一个指数η>；0>；0，使得Ω‘=H∩Ω∩U上的每个全纯函数f，其中dλ’表示H上的勒贝格测度，都可以被推广到Ω∩U上的全纯函数^f，使得即使
In this article a new contribution to the following question is given: Let Ω ⊂ ⊂ Cn be a bounded pseudoconvex domain with C∞-smooth boundary, q ∈ ∂Ω a fixed point and H a k-dimensional affine complex plane such that q ∈ H and H intersects ∂Ω at q transversally. Let U be a suitably small neighborhood of q, and denote by r a C∞-defining function of Ω on U. Under which conditions on ∂Ω near q is it possible to find an exponent η>0 > 0 such that every holomorphic function f on Ω′ = H ∩Ω∩ U with where dλ′ denotes the Lebesgue-measure on H, can be extended to a holomorphic function ^f on Ω ∩ U such that even