A Peak Set of Hausdorff Dimension 2n − 1 for the Algebra A(D) in the Boundary of a Domain D with C⌃2 Boundary

Abstract

We consider a bounded strictly pseudoconvex domain \(\Omega \subset \mathbb {C}^{n}\) with \(C^{2}\) boundary. Then, we show that any compact Ahlfors–David regular subset of \(\partial \Omega \) of Hausdorff dimension \(\beta \in (0,2n-1]\) contains a peak set E of Hausdorff dimension equal to \(\beta \).