On peak-interpolation manifolds for 𝐴(Ω) for convex domains in ℂ^{𝕟}

Let Ω \Omega be a bounded, weakly convex domain in C n {\mathbb {C}}^n , n ≥ 2 n\geq 2 , having real-analytic boundary. A ( Ω ) A(\Omega ) is the algebra of all functions holomorphic in Ω \Omega and continuous up to the boundary. A submanifold M ⊂ ∂ Ω \boldsymbol {M}\subset \partial \Omega is said to be complex-tangential if T p ( M ) T_p(\boldsymbol {M}) lies in the maximal complex subspace of T p ( ∂ Ω ) T_p(\partial \Omega ) for each p ∈ M p\in \boldsymbol {M} . We show that for real-analytic submanifolds M ⊂ ∂ Ω \boldsymbol {M}\subset \partial \Omega , if M \boldsymbol {M} is complex-tangential, then every compact subset of M \boldsymbol {M} is a peak-interpolation set for A ( Ω ) A(\Omega ) .