Peak-interpolating curves for A(Ω) for finite-type domains in C²

Gautam Bharali

Vol. 218 (2005), No. 2, 283–298

DOI: 10.2140/pjm.2005.218.283

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 ∈ 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 2000

Primary: 32A38, 32T25

Secondary: 32C25, 32D99

Milestones

Received: 2 December 2002

Revised: 20 April 2004

Published: 1 February 2005