| Abstract: | In the 1970’s, Folland and Stein studied a family of subelliptic scalar operators  which arise naturally in the  -complex. They introduced weighted Sobolev spaces as the natural spaces for this complex, and then obtained sharp estimates
for  in these spaces using integral kernels and approximate inverses. In the 1990’s, Rumin introduced a differential complex for
compact contact manifolds, showed that the Folland-Stein operators are central to the analysis for the corresponding Laplace
operator, and derived the necessary estimates for the Laplacian from the Folland Stein analysis. In this paper, we give a
self-contained derivation of sharp estimates in the anisotropic Folland-Stein spaces for the operators studied by Rumin using
integration by parts and a modified approach to bootstrapping.
This work was supported by NSERC (Grant No. RGPIN/9319-2005) |
