On products of some Toeplitz operators on polyanalytic Fock spaces. (English) Zbl 1513.47052

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.


47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
30H20 Bergman spaces and Fock spaces
30G30 Other generalizations of analytic functions (including abstract-valued functions)
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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