Sarason Conjecture on the Bergman space

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We provide a counterexample to the Sarason Conjecture for the Bergman space and present a characterisation of bounded Toeplitz products on the Bergman space in terms of test functions by means of a dyadic model approach. We also present some results about two-weighted estimates for the Bergman projection. Finally, we introduce the class B and give sharp estimates for the one-weighted Bergman projection.


Original languageEnglish
Pages (from-to)4320–4349
Number of pages30
JournalInternational Mathematics Research Notices
Issue number14
Early online date11 Jul 2016
Publication statusPublished - Jul 2017