Weighted spaces of holomorphic functions on the upper halfplane

  • Mohammad Ali Ardalani
  • Wolfgang Lusky

Abstract

We discuss weighted spaces $Hv(\mathbf{G})$ of holomorphic functions on the upper halfplane $\mathbf{G}$ where $v(w) = v(i \operatorname{Im} w)$, $w \in \mathbf{G}$, $\lim_{t\to 0} v(it)=0$ and $v(it)$ is increasing in $t$. We characterize those weights $v$ with moderate growth where $Hv(\mathbf{G})$ is isomorphic to $l_{\infty}$ and we show that this is never the case if $v$ is bounded.
Published
2012-12-01
How to Cite
Ardalani, M. A., & Lusky, W. (2012). Weighted spaces of holomorphic functions on the upper halfplane. MATHEMATICA SCANDINAVICA, 111(2), 244-260. https://doi.org/10.7146/math.scand.a-15226
Section
Articles