Abstract
Let X be a complex manifold of dimension n >= 3 and let 0 < q < n - 1. Let Omega(1) be a weakly q-convex and Omega(2) be a weakly (n - q - 1)-convex in X with smooth boundaries such that (Omega) over bar (2) (sic) Omega(1) (sic) X. Assume that b Omega(1) and b Omega(2) satisfy property (P). Then the compactness estimate for (p, q)-forms a holds for the (partial derivative) over bar -Neumann problem on the annulus domain Omega = Omega(1)\(Omega) over bar (2). Furthermore, if a is (partial derivative) over bar -closed (p, q)-form, which is C-infinity on (Omega) over bar and which is cohomologous to zero on Omega, the canonical solution u of the equation (partial derivative) over baru = alpha is smooth on (Omega) over bar.