Our purpose is to characterize the so-called horizontal Fock–Carleson type measures for derivatives of order k (we write it k-hFC for short) for the Fock space as well as the Toeplitz operators generated by sesquilinear forms given by them. We introduce real coderivatives of k-hFC type measures and show that the C*-algebra generated by Toeplitz operators with the corresponding class of symbols is commutative and isometrically isomorphic to a certain C*-subalgebra of L∞(ℝn). The above results are extended to measures that are invariant under translations along Lagrangian planes.
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To Nina Uraltseva, with best regards on her Jubilee
Translated from Problemy Matematicheskogo Analiza99, 2019, pp. 139-157.
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Esmeral, K., Rozenblum, G. & Vasilevski, N. 
–Invariant Fock–Carleson Type Measures for Derivatives of Order k and the Corresponding Toeplitz Operators.
J Math Sci 242, 337–358 (2019). https://doi.org/10.1007/s10958-019-04481-w
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DOI: https://doi.org/10.1007/s10958-019-04481-w