Toeplitz Operators on Fock Space $F_{\alpha }^{\mathrm{\infty }}$

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