Sarason Conjecture on the Bergman space

Alexandru Aleman; Sandra Pott; Maria Carmen Reguera

Sarason Conjecture on the Bergman space

Classical Analysis and ODEs 2013-09-05 v2 Complex Variables

Authors: Alexandru Aleman , Sandra Pott , Maria Carmen Reguera

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 $B_{\infty}$ and give sharp estimates for the one-weighted Bergman projection.

Keywords

bergman spaces tensor product banach spaces

Cite

@article{arxiv.1304.1750,
  title  = {Sarason Conjecture on the Bergman space},
  author = {Alexandru Aleman and Sandra Pott and Maria Carmen Reguera},
  journal= {arXiv preprint arXiv:1304.1750},
  year   = {2013}
}

Comments

31 pages. This version of the paper includes a counterexample to the Sarason Conjecture in the Bergman space

Sarason Conjecture on the Bergman space

Abstract

Keywords

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