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(uCφ) (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.