LAUSR

Let $$\mu $$μ be a normal functions on [0, 1), and H(B) be the space of all holomorphic functions on the unit ball B of $$\mathbf C^{n}$$Cn. Let $$\varphi $$φ be a nonconstant holomorphic self-map on B, and $$\psi $$ψ be a holomorphic function on B. The weighted differentiation composition operator $$\psi D_{\varphi }$$ψDφ is defined on the space H(B) by $$\psi D_{\varphi }(f)=\psi (Rf)\circ \varphi $$ψDφ(f)=ψ(Rf)∘φ, for all $$f\in H(B)$$f∈H(B). In this paper, the authors characterize the boundedness and compactness of the weighted differentiation composition operator $$\psi D_{\varphi }$$ψDφ from the normal weight Zygmund space $$Z_{\mu }(B)$$Zμ(B) to the normal weight Bloch space $$\beta _{\mu }(B)$$βμ(B) for $$n>1$$n>1. As a consequence of the main results, the authors give the briefly sufficient and necessary conditions that the differentiation composition operator $$ D_{\varphi }$$Dφ is compact from $$Z_{\mu }(B)$$Zμ(B) to $$\beta _{\mu }(B)$$βμ(B) for $$\displaystyle {\mu (r)=(1-r)^{s}\log ^{t}\frac{e}{1-r}}$$μ(r)=(1-r)slogte1-r.