Dual of the space of holomorphic functions with continuous boundary values on a strictly pseudoconvex domain in \({\mathbb{C}}^ n\) (Q1824069)

The paper gives the description of the dual of the space \({\mathcal A}(D)\) of holomorphic functions with continuous boundary values on a strictly pseudo-convex domain \(D\subset {\mathbb{C}}^ n\). The main result states that this dual space is isomorphic to the space of weakly continuous (n,n-1)- forms with Radon measure coefficients on \({\mathbb{C}}^ n\setminus D\), smooth and closed on \({\mathbb{C}}^ n\setminus \bar D\) that have at most first order poles along the plane at infinity. Several special cases are also treated.