Regularity of b complex on nondegenerate Cauchy-Riemann manifolds  

作　　者：WANG Wei 

出　　处：《Science China Mathematics》2001年第4期452-466,共15页中国科学：数学（英文版）

基　　金：This wore was supported by the National Natural Science Foundation of China (Grant No. 10071070) .

摘　　要：For each point ξ in a CR manifold M of codimension greater than 1, the CR structure of M can be approximated by the CR structure of a nilpotent Lie group Gξ of step two near ξ. Gξ varies with ξ. □b and b on M can be approximated by □4 and b on the nilpotent Lie group Gξ. We can construct the parametrix of □b on M by using the parametrix of □b on nilpotent group of step two, and define a quasidistance on M by the approximation. The regularity of □b and b follows from the Harmonic analysis on M.<正>For each point ξ in a CR manifold M of codimension greater than 1, the CR structure of M can be approximated by the CR structure of a nilpotent Lie group Gξ of step two near ξ. Gξ varies with ξ. □b and b on M can be approximated by □4 and b on the nilpotent Lie group Gξ. We can construct the parametrix of □b on M by using the parametrix of □b on nilpotent group of step two, and define a quasidistance on M by the approximation. The regularity of □b and b follows from the Harmonic analysis on M.

关 键 词：nilpotent Lie group of step two b complex Kohn Laplacian □b parametrix integral operator of l type. 

分 类 号：O17[理学—数学]