Stein流形上Cauchy-Riemann方程的具有权的基本解  

Fundamental Solutions with Weight Factors of Cauchy-Riemann Equations on Stein Manifolds

作　　者：邱春晖[1] 

机构地区：[1]厦门大学数学系

出　　处：《厦门大学学报（自然科学版）》1992年第2期111-115,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金;福建省自然科学基金

摘　　要：利用陈度量和陈联络,作者构造了Stein流形上(p,q)微分形式的具有权的B-M核B(z,ζ)、Leray核L(z,ζ)、Henkin核H(z,ζ)和核T(z,ζ)以及微分形式P(z,ζ),并利用局部化技巧,证明了这些核的积分主值是存在的,以及核B、L—B+T和B(f∧H)是Cauchy-Riemann方程=[△]+P的基本解,作者还讨论了与这些核相应的算子L、H和T的奇点的传播。By using Chern metric and connection, the B-M kernel B,Leray kernel L,Henkin kernel H with weight factors, a kernel T and a differential form P are constructed on a Stein manifold. Using the technique of localization, the author proves that the principal value of integral with kernel B,L and H exist respectively, and that the kernel B,L-B+T and B + (?)(f∧H) satisfy the fundamental equation (?)E=[Δ]+P respectively. Further, the author discusses the propagation of singularities of the operators L,H and T which are induced by kernels L,H and T respectively.

关 键 词：STEIN流形 C-R方程 积分主值 

分 类 号：O174.56[理学—数学]