Toeplitz operators between distinct Bergman spaces

In this paper, we provide descriptions of the boundedness and compactness for the Toeplitz operators Tμ,β between distinct weighted Bergman spaces Lap(ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_a^p\left(\omega \right)$$\end{document} and Laq(ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_a^q\left(\omega \right)$$\end{document} for 0 < p ⩽ 1, q = 1, −1 < α, β < ∞ and 0 < p ⩽ 1 < q < ∞, −1 < β ⩽ α < ∞, respectively. Part of our results are new even in the unweighted Bergman spaces.