2019/04/24 by Coacalle, Joel, Raich, Andrew
#32F17 #32V20 #32W10 (Primary) #35A27 #35N15 (Secondary) #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1904.10836
The purpose of this paper is to establish sufficient conditions for closed range estimates on (0,q)-forms, for some fixed q, 1 ≤ q ≤ n-1, for ∂b in both L2 and L2-Sobolev spaces in embedded, not necessarily pseudoconvex CR manifolds of hypersurface type. The condition, named weak Y(q), is both more general than previously established sufficient conditions and easier to check. Applications of our estimates include estimates for the Szegö projection as well as an argument that the harmonic forms have the same regularity as the complex Green operator. We use a microlocal argument and carefully construct a norm that is well-suited for a microlocal decomposition of form. We do not require that the CR manifold is the boundary of a domain. Finally, we provide an example that demonstrates that weak Y(q) is an easier condition to verify than earlier, less general conditions.