SPACES OF ANALYTIC FUNCTIONS IN HYPERCONVEX DOMAINS IN Cn
Michael I. Stessin
Department of Mathematics and Statistics
State University of New York University at Albany
Albany, NY 12222 – USA
stessin@math.albany.edu
We use the Lelong-Jensen formula proved by Demailly to de¯ne the scale of weighted Bergman spaces corresponding to a plurisubharmonic exhaustion of a hyperconvex domain in Cn and extend results proved in the classical theory to this setting. In the case when the chosen exhaustion is a Green function of the Monge-Ampere operator the results take a form similar to the ones proved in the classical theory for spaces of analytic functions in the unit disk, or such domains as balls and polydisks. We will also consider a construction of an analog of the Nevanlinna counting function, its connection to the introduced norms and composition operators acting on spaces of analytic functions in hyperconvex domains. The talk is based on a joint work with E.A.Poletsky.
