Stein流形上凸区域的边界性质

The Boundary Behaviour on a Convex Domain in a Stein Manifold

研究Ｃｎ 空间和Ｓｔｅｉｎ 流形上凸区域的边界性质．利用局部化技巧和Ｃｎ 空间中凸区域的СохоцкｕｕＶ－Ｐｌｅｍ ｅｌｊ公式，定义Ｓｔｅｉｎ流形上具有Ａｉｚｅｎｂｅｒｇ核的Ｃａｕｃｈｙ型积分的奇异积分的Ｃａｕｃｈｙ主值，得到如下的Ｓｔｅｉｎ 流形上凸区域的СохоцкｕｕＶ－Ｐｌｅｍ ｅｌｊ公式 Ｆ＋ （η） ＝ Ｖ．Ｐ．∫Ｍξｆ（ξ）Ｋ（η，ξ） ＋ １２ ｆ（η），η∈Ｍ Ａ－ （η） ＝ Ｖ．Ｐ．∫Ｍξα（ξ）ＴＫ（η，ξ） － １２ α（η），η∈Ｍ这里，ｆ（ξ） ∈Ｄ０，０（Ｍ）．α（ξ） ∈Ｄｎ，ｎ－ １（Ｍ），Ｍ 为凸区域的边界．

The boundary behaviour on a convex domain in C n and a Stein manifold is studied. By using the technique of localization and the Coxoцкu u∨ Plemelj formula on a convex domain in C n , Cauchy principal values of singular integrals of Cauchy type integrals with Aizerberg kernel in a Stein manifold are defined and the Coxoцкu uV Plemelj formula on a convex domain in a Stein manifold is obtained as follows: F +(η)= V.P .∫ M ξ f(ξ)K(η,ξ)+12f(η),η∈M, A -(η)= V.P .∫ M ξ α(ξ) TK(η,ξ)-12α(η),η∈M, where, f(ξ)∈D 0,0 (M),α(ξ)∈D n,n-1 (M), M is the boundary of the convex domain.