Weighted composition operators on spaces of analytic functions on the complex half-plane

Andrzej S. Kucik

Published 2016-10-03Version 1

In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane, which include Hardy space, weighted Bergman spaces and Dirichlet space, can be stated in terms of Carleson measures and Bergman kernels. In Hilbertian setting we will also show how the norms of causal weighted composition operators on these spaces are related to each other and use it to show that an (unweighted) composition operator $C_\varphi$ is bounded on a Zen space if and only if $\phi$ has a finite angular derivative at ininity. Finally, we will show that there is no compact composition operator on Zen spaces.