The complex Green operator on CR-submanifolds of C n mathbb {C}^{n} of hypersurface type: Compactness Academic Article uri icon

abstract

  • We establish compactness estimates for ∂ b on a compact pseudo convex CR-sub manifold of C n of hyper surface type that satisfies property(P). When the sub manifold is orientable, these estimates were proved by A. Raich in 2010 using micro local methods. Our proof deduces the estimates from (a slight extension, when q > 1, of) those known on hyper surfaces via the fact that locally, CR-sub manifolds of hyper surface type are CR-equivalent to a hyper surface. The relationship between two potential theoretic conditions is also clarified. © 2012 American Mathematical Society.

author list (cited authors)

  • Straube, E. J.

citation count

  • 6

publication date

  • August 2012