Interpolation in weakly pseudoconvex domains in \({\mathbb{C}}^ 2\) (Q790302)

Let \(D\subset \subset {\mathbb{C}}^ 2\) be a pseudoconvex domain with smooth boundary and of finite type, and let \(M\subset \partial D\) be a smooth curve which is locally a peak set for \(A^{\infty}(D)\). (a) If \(\partial D\) is of constant type along M, then every compact subset of M is an interpolation set for \(A^{\infty}(D)\). (b) If \(\partial D\) and M are real-analytic, then every compact subset of M is an interpolation set for \(A^{\infty}(D).\) In addition, an example is given of a convex domain \(D\subset \subset {\mathbb{C}}^ 2\) with smooth boundary whose weakly pseudoconvex boundary points form a line segment K so that K is a peak set for \(A^{\infty}(D)\) but K is not locally an interpolation set for \(A^{\infty}(D)\). K consists of points of infinite type.