–Invariant Fock–Carleson Type Measures for Derivatives of Order k and the Corresponding Toeplitz Operators

Abstract

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.