Estimates for the \(\bar\partial\)-Neumann problem in the Sobolev topology on \(Z(q)\) domains (Q2747328)

We quote the authors' abstract: This paper is the continuation of [\textit{L. Fontana}, \textit{S. Krantz} and \textit{M. Peloso}, Indiana Univ. Math. J. 48, No. 1, 275-293 (1999; Zbl 0994.35099)], where the \(\overline \partial\)-Neumann problem in the Sobolev topology is formulated and studied on pseudoconvex domains in \(\mathbb{C}^n\).NEWLINENEWLINENEWLINEIn this paper we study the \(\overline \partial\)-Neumann problem in the topology of \(W^1\) on a domain of the so-called class \(Z(q)\). The appropriate non-coercive condition on the corresponding bilinear form \(Q\) is proved. Optimal estimates for the \(\overline \partial\)-Neumann problem are then derived. The result is a new canonical solution for the \(\overline \partial\)-problem giving best possible estimates and a new Hodge theory for the Cauchy-Riemann complex.