Schatten–Herz Classes of Toeplitz Operators on the Generalized Fock Space

Abstract

Let F 2 ϕ be the generalized Fock space defined aswhere ϕ is some fixed weight function satisfying M 1 ω 0 ≤ dd c ϕ ≤ M 2 ω 0 . Given 0 < p ≤ ∞ and 0 ≤ q ≤ ∞, as an extension of Schatten class Toeplitz operators we introduce the concept of Schatten-Herz class Toeplitz operators S p,q on F 2 ϕ . We also characterize those positive Borel measures μ on C n for which the induced Toeplitz operators T μ belong to S p,q .