On Toeplitz Operators Between Fock Spaces

We study some mapping properties of Toeplitz operators Tμ associated with nonnegative Borel measures μ on the complex space Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}^n}$$\end{document}. In particular, we describe the bounded and compact properties of Tμ acting between Fock spaces in terms of the objects t-Berezin transforms, averaging functions, and averaging sequences of μ. We also obtain an asymptotic estimate for the norms of the operators. The results extend and complete a recent work of Z. Hu and X. Lv when both the smallest and the largest Banach–Fock spaces are taken into account.