In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz esti...In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained.展开更多
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 ca...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.展开更多
基金the Graduate Student Innovation Fund of Fudan University.
文摘In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained.
基金This wore was supported by the National Natural Science Foundation of China (Grant No. 10071070) .
文摘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.
