Regularity of b complex on nondegenerate Cauchy-Riemann manifolds

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.