Regularity results for ${\bar{\partial }}_b$ on CR-manifolds of hypersurface type

Abstract

We introduce a class of embedded CR manifolds satisfying a geometric condition that we call weak $Y(q)$. For such manifolds, we show that dbar-b has closed range on $L^2$ and that the complex Green operator is continuous on $L^2$. Our methods involves building a weighted norm from a microlocal decomposition. We also prove that at any Sobolev level there is a weight such that the complex Green operator inverting the weighted Kohn Laplacian is continuous. Thus, we can solve the dbar-b equation in $C^{\infty }$.

arXiv comment23 pages

References in corpus (1)

• Compactness of the Complex Green Operator on CR-Manifolds of Hypersurface Type