Abstract
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.
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Chalendar, I., Partington, J.R. The reproducing kernel thesis for lower bounds of weighted composition operators. Arch. Math. 113, 179–187 (2019). https://doi.org/10.1007/s00013-019-01323-8
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DOI: https://doi.org/10.1007/s00013-019-01323-8
Keywords
- Reproducing kernel
- Weighted composition operator
- Reverse Carleson measure
- Hardy space
- Bergman space
- Test functions