Weighted spaces of holomorphic functions on the upper halfplane - Ardalani, Mohammad Ali; Lusky, Wolfgang (MATHEMATICA SCANDINAVICA, 2012)
We discuss weighted spaces $Hv(G)$ of holomorphic functions on the upper halfplane $G$ where $v(w) = v(i \operatorname{Im} w)$, $w \in G$, $\lim_{t→ 0} v(it)=0$ and $v(it)$ is increasing in $t$. We characterize those weights $v$ with moderate growth where $Hv(G)$ is isomorphic to $l_{∞}$ and we show that this is never the case if $v$ is bounded.