We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW. These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-4,
author = {M. Jasiczak},
title = {On locally convex extension of $H^{$\infty$}$ in the unit ball and continuity of the Bergman projection},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {261-275},
zbl = {1026.32007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-4}
}
M. Jasiczak. On locally convex extension of $H^{∞}$ in the unit ball and continuity of the Bergman projection. Studia Mathematica, Tome 157 (2003) pp. 261-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-4/