On analytic interpolation manifolds in boundaries of weakly pseudoconvex domains

Abstract

Let $\Omega$ be a bounded, weakly pseudoconvex domain in C^n, n > 1, with real-analytic boundary. A real-analytic submanifold $M\subset bd\Omega$ is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to $\Cal{O}(\barΩ)$. We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of $bd\Omega$.

Final version: corrected statement of Burns-Stout theorem and typos in Example 4.5; added Remark 1.5