Weighted Differentiation Composition Operators Between Normal Weight Zygmund Spaces and Bloch Spaces in the Unit Ball of Cn for n > 1

摘要

Let be a normal functions on [0,1), and H(B) be the space of all holomorphic functions on the unit ball B of Cn. Let phi be a nonconstant holomorphic self-map on B, and be a holomorphic function on B. The weighted differentiation composition operator D phi is defined on the space H(B) by D phi(f)=(Rf)degrees phi, for all fH(B). In this paper, the authors characterize the boundedness and compactness of the weighted differentiation composition operator D phi from the normal weight Zygmund space Z(B) to the normal weight Bloch space (B) for n>1. As a consequence of the main results, the authors give the briefly sufficient and necessary conditions that the differentiation composition operator D phi is compact from Z(B) to (B) for w mu(r) = (1 - r) s log(t) e/1-r.