Pseudoconvex domains with peak functions at each point of the boundary (Q1089475)

Let D be a bounded pseudoconvex domain in \({\mathbb{C}}^ n\) with \(C^{\infty}\) boundary and let \(A^{\infty}(D)\) be the algebra of holomorphic functions in D which have a \(C^{\infty}\) extension to \=D. If D is strictly pseudoconvex, it is a very known result of H. Rossi that each point of the boundary is a peak point for \(A^{\infty}(D)\). This happens also if D is weakly pseudoconvex and the weakly pseudoconvex boundary points are of strict type. In this paper, there are given other conditions on the set of weakly pseudoconvex boundary points of a pseudoconvex domain in \({\mathbb{C}}^ n\), which ensure that each point of the boundary is a peak point for \(A^{\infty}(D)\).