Local Sobolev—Bergman Kernels of Strictly Pseudoconvex Domains
Local Sobolev—Bergman Kernels of Strictly Pseudoconvex Domains
复制标题
局部 Sobolev—严格伪凸域的 Bergman 核
DOI：
10.1007/978-1-4612-2166-1_5
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发表时间：
1999
影响因子：
4.9
通讯作者：
G. Komatsu
中科院分区：
文献类型：
--
作者：
K. Hirachi;G. Komatsu
这篇文章的目的是试图理解February man的Bergman核在Ω × Ω对角线上的不变量理论[F3]的分析方面，对于具有光滑（C ∞或真实的解析）边界的严格伪凸域Ω，February man的不变量理论[F3]。他的不变理论的框架同样适用于Szego核，如果适当选择的表面元素对Ω，而Szego核被视为再生核的希尔伯特空间的全纯函数在Ω属于L 2索伯列夫空间的秩序1/2。这一事实是我们的出发点。对任意s ∈ H，我们首先定义s/2阶Sobolev-Bergman核Ks为s/2阶L2 Sobolev空间中全纯函数的Hilbert空间HS/2（Ω）的再生核，其中内积是任意给定的.
This article grew out of an attempt to understand analytic aspects of Fefferman’s invariant theory [F3] of the Bergman kernel on the diagonal of Ω × Ω for strictly pseudoconvex domains Ω in ℂ n with smooth (C ∞ or real analytic) boundary. The framework of his invariant theory applies equally to the Szego kernel if the surface element on ∂Ω is appropriately chosen, while the Szego kernel is regarded as the reproducing kernel of a Hilbert space of holomorphic functions in Ω which belong to the L 2 Sobolev space of order 1/2. This fact is our starting point. For each s ∈ ℝ, we first globally define the Sobolev-Bergman kernel K s of order s/2 to be the reproducing kernel of the Hilbert space H S /2(Ω) of holomorphic functions which belong to the L 2 Sobolev space of order s/2, where the inner product is specified arbitrarily.