Weighted Differentiation Composition Operator from Logarithmic Bloch Spaces to Zygmund-Type Spaces

Abstract EN

Let H ( ? ) denote the space of all holomorphic functions on the unit disk ? of ℂ , u ∈ H ( ? ) and let n be a positive integer, φ a holomorphic self-map of ? , and μ a weight.

In this paper, we investigate the boundedness and compactness of a weighted differentiation composition operator ? φ , u n f ( z ) = u ( z ) f ( n ) ( φ ( z ) ) , f ∈ H ( ? ) , from the logarithmic Bloch spaces to the Zygmund-type spaces.