The reproducing kernel thesis for lower bounds of weighted composition operators

  • I. Chalendar
  • J. R. PartingtonEmail author
Open Access


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.


Reproducing kernel Weighted composition operator Reverse Carleson measure Hardy space Bergman space Test functions 

Mathematics Subject Classification

47B33 30H10 32A36 47B32 



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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Université Paris Est, LAMA, (UMR 8050), UPEM, UPEC, CNRSMarne-la-ValléeFrance
  2. 2.School of MathematicsUniversity of LeedsLeedsUK

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