Composition operators on weighted spaces of holomorphic functions on the upper half plane - Lusky, Wolfgang (MATHEMATICA SCANDINAVICA, 2018)
We consider moderately growing weight functions v on the upper half plane G called normal weights which include the examples (Im w)^a, w 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_φ on the weighted spaces Hv(G). We characterize those holomorphic functions φ G → G where the composition operator C_φ is a bounded operator Hv(G) → Hv(G) by a simple property which depends only on φ but not on v. Moreover we show that there are no compact composition operators C_φ on Hv(G).