The reproducing kernel thesis for lower bounds of weighted composition operators

Isabelle Chalendar, Jonathan R. Partington

Published 2018-12-19Version 1

It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The methods used in the analysis are based on the theory of reverse Carleson embeddings.