On locally convex extension of $H^{\infty }$ in the unit ball and continuity of the Bergman projection
Tom 156 / 2003
Studia Mathematica 156 (2003), 261-275
MSC: 32A25, 32A36, 32A70, 46A13, 46E10.
DOI: 10.4064/sm156-3-4
Streszczenie
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 $HW$.
