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Sarason conjecture on the Bergman space

Aleman, Alexandru LU ; Pott, Sandra LU and Reguera Rodriguez, Maria Del Carmen LU (2017) In International Mathematics Research Notices 2017(14). p.4320-4349
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.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Mathematics Research Notices
volume
2017
issue
14
pages
30 pages
publisher
Oxford University Press
external identifiers
  • scopus:85104416460
ISSN
1073-7928
DOI
10.1093/imrn/rnw134
language
English
LU publication?
yes
id
c6034781-eeae-4939-8623-050b2f2554c3
date added to LUP
2019-05-24 18:48:36
date last changed
2025-10-14 10:08:30
@article{c6034781-eeae-4939-8623-050b2f2554c3,
  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.}},
  author       = {{Aleman, Alexandru and Pott, Sandra and Reguera Rodriguez, Maria Del Carmen}},
  issn         = {{1073-7928}},
  language     = {{eng}},
  number       = {{14}},
  pages        = {{4320--4349}},
  publisher    = {{Oxford University Press}},
  series       = {{International Mathematics Research Notices}},
  title        = {{Sarason conjecture on the Bergman space}},
  url          = {{http://dx.doi.org/10.1093/imrn/rnw134}},
  doi          = {{10.1093/imrn/rnw134}},
  volume       = {{2017}},
  year         = {{2017}},
}