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\begin{document}$${\mathbb {B}}$$\end{document} be an open unit ball in Cn.\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {C}}^{n}.$$\end{document} Let H(B)\documentclass[12pt]{minimal}
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\begin{document}$$H({\mathbb {B}})$$\end{document} be the collection of all analytic functions on B\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {B}}$$\end{document} and S(B)\documentclass[12pt]{minimal}
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\begin{document}$$S({\mathbb {B}})$$\end{document} be the collection of all analytic self-maps on B.\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {B}}.$$\end{document} In this paper, we study the boundedness and compactness of the operator Tψ0,ψ1,ψ2,φf(z)=ψ0(z)f(φ(z))+ψ1(z)Rf(φ(z))+ψ2(z)R(f∘φ)(z),\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} T_{\psi _0,\psi _1,\psi _2,\varphi }f(z)=\psi _{0}(z)f(\varphi (z))+ \psi _{1}(z){\mathcal {R}}f(\varphi (z))+\psi _2(z) {\mathcal {R}}(f\circ \varphi )(z), \end{aligned}$$\end{document}where ψ0,ψ1,ψ2∈H(B),\documentclass[12pt]{minimal}
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\begin{document}$$\psi _0,\psi _1,\psi _2\in H({\mathbb {B}}),$$\end{document}φ∈S(B)\documentclass[12pt]{minimal}
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\begin{document}$$\varphi \in S({\mathbb {B}})$$\end{document} and Rf\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {R}}f$$\end{document} denotes the radial derivative of f∈H(B),\documentclass[12pt]{minimal}
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\begin{document}$$f\in H({\mathbb {B}}),$$\end{document} from a class of Banach spaces of analytic functions to μ\documentclass[12pt]{minimal}
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\begin{document}$$\mu $$\end{document}-Bloch spaces on B\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {B}}$$\end{document} and obtain estimates for its norm.
