Sarason Conjecture on the Bergman space

By Alexandru Aleman, Sandra Pott, M. Reguera. 2013

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

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/129e08f0347940da5d29fed00b8c03c3d3e69be7