Toeplitz Operators on Fock Space $F_{\hat{I}}{\pm }^{\infty }$

Abstract

In this paper, we study necessary and sufficient conditions for a positive Borel measure $\hat{I}¼$ on the complex space $\mathbb{C}$ to be a $(\infty ,q)$ or $(p,\infty )$ (vanishing) Fock-Carleson measure through its Berezin transform. Then we discuss boundedness and compactness of the Toeplitz operator $T_{\hat{I}}¼$ with a positive Borel measure $\hat{I}¼$ as symbol on Fock space $F_{\hat{I}}{\pm }^{\infty }$. Furthermore, we charaterize these properties of the Toeplitz operator T_φ$withasymbol$φ$whichisin$BMO$.

11pages