Weighted composition operators from Zygmund spaces into Bloch spaces

Abstract

Let φ be an analytic self-map and u be a fixed analytic function on the open unit disk D in the complex plane C . The weighted composition operator is defined by ( uC φ ) ( f ) ( z ) = u ( z ) f ( φ ( z ) ) , z ∈ D , f ∈ H ( D ) . This paper studies the boundedness and compactness of weighted composition operators from Zygmund spaces into Bloch spaces.