Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 369-379, 2020
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
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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: irene.casseli@univ-amu.fr
