@article{Lusky_2018, title={Composition operators on weighted spaces of holomorphic functions on the upper half plane}, volume={122}, url={https://www.mscand.dk/article/view/97126}, DOI={10.7146/math.scand.a-97126}, abstractNote={<p>We consider moderately growing weight functions $v$ on the upper half plane $\mathbb G$ called normal weights which include the examples $(\mathrm{Im} w)^a$, $w \in \mathbb G$, for fixed $a &gt; 0$. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators $C_{\varphi }$ on the weighted spaces $Hv(\mathbb G)$. We characterize those holomorphic functions $\varphi \colon \mathbb G \rightarrow \mathbb G$ where the composition operator $C_{\varphi } $ is a bounded operator $Hv(\mathbb G) \rightarrow Hv(\mathbb G)$ by a simple property which depends only on $\varphi $ but not on $v$. Moreover we show that there are no compact composition operators $C_{\varphi }$ on $Hv(\mathbb G)$.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Lusky, Wolfgang}, year={2018}, month={Feb.}, pages={141–150} }