On Products of Some Toeplitz Operators on Polyanalytic Fock Spaces


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 TfT subjected to certain restriction on f and g. We also characterize this property in terms of the Berezin transform.

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This work is part of my PhD thesis. I am grateful to my advisers Professors S. Rigat and E. H. Youssfi for suggesting this problem and for helpful discussions.

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Correspondence to Irène Casseli.

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Casseli, I. On Products of Some Toeplitz Operators on Polyanalytic Fock Spaces. Czech Math J 70, 369–379 (2020). https://doi.org/10.21136/CMJ.2019.0334-18

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  • polyanalytic function
  • Toeplitz operator
  • Fock space
  • Sarason’s problem

MSC 2010

  • 47B35
  • 30H20
  • 30G30
  • 46E22