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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## 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 $HW$.

#### Autorzy

• M. JasiczakFaculty of Mathematics and Computer Science