Toeplitz operators on the Fock spaces F_α^p

In this paper, enlightened by Isralowitz’s works on the properties of weakly localized operators on Fock spaces, we use Berezin transform as a key tool to investigate boundedness and compactness of Toeplitz operators T_φ with symbols φ in BMO on the Fock spaces F_α^p(1＜p＜+∞). We extend properties of T_φ on F_α^2 to the more general F_α^p setting, yielding two main results: T_φ is a bounded operator on F_α^p if and only if the Berezin transform \widetilde\varphi of φ is bounded, T_φ is a compact operator on F_α^p if and only if \widetilde\varphi∈C₀(\mathbbC). If φ is harmonic function of BMO, then T_φ is bounded on F_α^p if and only if φ is bounded, T_φ is compact on if and only if φ∈C₀（\mathbbC）.