Composition operators on weighted spaces of holomorphic functions on the upper half plane

Authors

  • Wolfgang Lusky

DOI:

https://doi.org/10.7146/math.scand.a-97126

Abstract

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 $a > 0$. 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 $Hv(\mathbb G)$.

References

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Published

2018-02-20

How to Cite

Lusky, W. (2018). Composition operators on weighted spaces of holomorphic functions on the upper half plane. MATHEMATICA SCANDINAVICA, 122(1), 141–150. https://doi.org/10.7146/math.scand.a-97126

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Articles