Sarason Conjecture on the Bergman space

A Aleman; Sandra Pott; Maria Carmen Reguera

doi:10.1093/imrn/rnw134

Sarason Conjecture on the Bergman space

A Aleman, Sandra Pott, Maria Carmen Reguera

Mathematics

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Abstract

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 language	English
Pages (from-to)	4320–4349
Number of pages	30
Journal	International Mathematics Research Notices
Volume	2017
Issue number	14
Early online date	11 Jul 2016
DOIs	https://doi.org/10.1093/imrn/rnw134
Publication status	Published - Jul 2017

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10.1093/imrn/rnw134Licence: None: All rights reserved

AlemanA2017Sarason
This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record, Alexandru Aleman, Sandra Pott, Maria Carmen Reguera, Sarason Conjecture on the Bergman Space, International Mathematics Research Notices, Volume 2017, Issue 14, July 2017, Pages 4320–4349, is available online at: https://doi.org/10.1093/imrn/rnw134
Accepted author manuscript, 389 KBLicence: None: All rights reserved

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AB - 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.

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JO - International Mathematics Research Notices

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Sarason Conjecture on the Bergman space

Abstract

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