Duality and the Class of Holomorphic Functions Representable by Carleman’s Formula

The purpose of the present paper is two-fold. The first is to describe the space of continuous functionals for the Smirnov space Ep(U), p ≥ 1, when U is a simply connected, bounded domain with Ahlfors regular boundary in terms of functions which are analytic in the complement U (or dual complement) and have a prescribed boundary behavior on ∂U . As an application of the above results, we give a precise description of the space of continuous functionals acting on the space NH M (U), p ≥ 1 of holomorphic functions representable by Carleman’s formula. Similar results are proven for topological products of bounded simply connected domains with Ahlfors regular boundaries.