Abstract

Let Ω be a bounded, weakly pseudoconvex domain in C², having smooth boundary. A(Ω) is the algebra of all functions holomorphic in Ω and continuous up to the boundary. A smooth curve C ⊂ ∂Ω is said to be complex-tangential if T_p(C) lies in the maximal complex subspace of T_p(∂Ω) for each p in C. We show that if C is complex-tangential and ∂Ω is of constant type along C, then every compact subset of C is a peak-interpolation set for A(Ω). Furthermore, we show that if ∂Ω is real-analytic and C is an arbitrary real-analytic, complex-tangential curve in ∂Ω, compact subsets of C are peak-interpolation sets for A(Ω).

Keywords

complex-tangential, finite type domain, interpolation set, pseudoconvex domain

Mathematical Subject Classification

Primary: 32A38, 32T25

Secondary: 32C25, 32D99

Authors