Estimates for the (delta)over-bar-Neumann problem in the Sobolev topology on Z(q) domains

This paper is the continuation of [FKP2], where the ∂̄-Neumann problem in the Sobolev topology is formulated and studied on pseudoconvex domains in ℂn. In this paper we study the ∂̄-Neumann problem in the topology of W1 on a domain of the so-called class Z(q). The appropriate noncoercive condition on the corresponding bilinear form Q is proved. Optimal estimates for the ∂̄-Neumann problem are then derived. The result is a new canonical solution for the ∂̄ problem giving best possible estimates and a new Hodge theory for the Cauchy-Riemann complex.