Extension of vector-valued holomorphic and harmonic functions

Abstract

We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak'-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, HoItmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces. © Instytut Matematyczny PAN, 2007.