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Keywords:
polyanalytic function; Toeplitz operator; Fock space; Sarason's problem
polyanalytic function; Toeplitz operator; Fock space; Sarason's problem
Summary:
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_{f}T_{\bar g}$ subjected to certain restriction on $f$ and $g$. We also characterize this property in terms of the Berezin transform.
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