The Ohsawa-Takegoshi extension theorem on some unbounded sets

Abstract

We use a method of Berndtsson to obtain a simplification of Ohsawa's result concerning extension of $L^{2}$-holomorphic functions. We also study versions of the Ohsawa-Takegoshi theorem for some unbounded pseudoconvex domains, with an application to the theory of Bergman spaces. Using these methods we improve some constants, that arise in related inequalities.