# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On the boundedness of the differentiation operator between weighted spaces of holomorphic functions

### Tom 184 / 2008

Studia Mathematica 184 (2008), 233-247 MSC: Primary 46E15; Secondary 47B38. DOI: 10.4064/sm184-3-3

#### Streszczenie

We give necessary and sufficient conditions on the weights $v$ and $w$ such that the differentiation operator $D: Hv( \Omega) \rightarrow Hw( \Omega)$ between two weighted spaces of holomorphic functions is bounded and onto. Here $\Omega = \mathbb C$ or $\Omega = \mathbb D$. In particular we characterize all weights $v$ such that $D:Hv( \Omega) \rightarrow Hw( \Omega)$ is bounded and onto where $w(r) = v(r)(1-r)$ if $\Omega = \mathbb D$ and $w=v$ if $\Omega = \mathbb C$. This leads to a new description of normal weights.

#### Autorzy

• Anahit HarutyunyanFaculty for Informatics and Applied Mathematics
University of Yerevan
Alek Manukian 1
Yerevan 25, Armenia
e-mail
• Wolfgang LuskyInstitute for Mathematics
University of Paderborn
Warburger Str. 100
D-33098 Paderborn, Germany
e-mail

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