GLOBAL REGULARITY OF THE PARTIAL-DERIVATIVE-NEUMANN PROBLEM ON AN ANNULUS BETWEEN 2 PSEUDOCONVEX MANIFOLDS WHICH SATISFY PROPERTY-(P)

Let X be a complex manifold of dimension n greater than or equal to 3. Let Omega(1), Omega(2) be two open pseudoconvex submanifolds with smo oth boundary such that Omega(1) ... Omega(2) ... X. Let Omega = <Omega (2)\(Omega)over bar (1)>. Assume that b Omega(1) and b Omega(2) satisf y Catlin's condition (P). Then the compactness estimate for (p, q)-for ms with 0 < q < n - 1 holds for the <(partial derivative)over bar -Neu mann> problem on Omega. This result implies that given a <(partial der ivative)over bar -closed> (p, q)-form alpha with 0 < q < n - 1, which is C-infinity on <(Omega)over bar> and which is cohomologous to zero o n Omega, the canonical solution u of the equation <(partial derivative )over bar u> = or is smooth on <(Omega)over bar>.