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, Holtmanns 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-3-2,
author = {Jos\'e Bonet and Leonhard Frerick and Enrique Jord\'a},
title = {Extension of vector-valued holomorphic and harmonic functions},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {225-248},
zbl = {1141.46017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-3-2}
}
José Bonet; Leonhard Frerick; Enrique Jordá. Extension of vector-valued holomorphic and harmonic functions. Studia Mathematica, Tome 178 (2007) pp. 225-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-3-2/