Czechoslovak Mathematical Journal, first online, pp. 1-11

On products of some Toeplitz operators on polyanalytic Fock spaces

Irène Casseli

Received July 13, 2018.   Published online November 27, 2019.

Abstract:  The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz products $ T_fT_{\bar g}$ subjected to certain restriction on $f$ and $g$. We also characterize this property in terms of the Berezin transform.
Keywords:  polyanalytic function; Toeplitz operator; Fock space; Sarason's problem
Classification MSC:  47B35, 30H20, 30G30, 46E22
DOI:  10.21136/CMJ.2019.0334-18

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Affiliations:   Irène Casseli, Aix-Marseille Université, I2M UMR CNRS 7373, 39 Rue F. Joliot-Curie, 13453 Marseille Cedex 13, France, e-mail:

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