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

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