On a new class of operators from the Bloch-type space into H∞(BX)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H^{\infty}(\mathbb{B}_{X})$\end{document} of infinite dimensional bounded symmetric domains

Under certain assumptions on the symbols, we give a necessary and sufficient condition for the boundedness of a new class of operators, Tψ1,ψ2,ψ3,φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{\psi _{1}, \psi _{2}, \psi _{3}, \varphi}$\end{document}, mapping from the Bloch-type space B(BX)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{B}(\mathbb{B}_{X})$\end{document} into the space of bounded holomorphic function H∞(BX)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H^{\infty}(\mathbb{B}_{X})$\end{document} of infinite-dimensional bounded symmetric domains. Moreover, we establish a sufficient condition for the boundedness of the operator Tψ1,ψ2,ψ3,φ:B0(BX)→Hμ,0∞(BX)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{\psi _{1}, \psi _{2}, \psi _{3}, \varphi}: \mathcal{B}_{0}(\mathbb{B}_{X})\rightarrow H_{\mu , 0}^{\infty}(\mathbb{B}_{X})$\end{document}.