Toeplitz operators between generalized Fock spaces

Abstract

In this paper, for $0＜p\leq \infty$, we consider Toeplitz operators with positive Borel measure symbols between $F^p_{\varphi}$ and $F^{\infty}_{\varphi}$, where $\varphi\in C^2(\C^n)$ satisfies $0＜m\leq \triangle\varphi\leq M$ for positive constants $m$ and $M$. We use Carleson measures and $t$-Berezin transforms to characterize boundedness and compactness of those operators. This work extends and completes the main results of Mengesite, Hu and Lv. Toeplitz operators between $F^p_{\varphi}$ and $F^{\infty}_{\varphi}$ with $0＜p＜1,$ $p=\infty$ have not been studied before even for classic Fock space setting.