Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carathéodory Domains

Abstract

The spaces dual to spaces of holomorphic functions of given growth on Carathéodory domains are described by using the Cauchy transform of functionals. A pseudoanalytic extension of such transforms to the whole plane is constructed, which makes it possible to remove convexity constrains and consider spaces determined by weights of general form, rather than only by those whose dependence on the distance from a point of the domain to its boundary is one-dimensional.