Weighted composition operators from Bergman-type spaces into Bloch spaces

TL;DR

This paper characterizes weighted composition operators from Bergman-type spaces to Bloch spaces using properties of their inducing maps, advancing understanding of operator behavior in complex analysis.

Contribution

It provides a new characterization of weighted composition operators between specific function spaces based on the properties of the inducing maps.

Findings

Characterization of weighted composition operators from Bergman-type to Bloch spaces.

Identification of conditions on the inducing maps for boundedness and compactness.

Extension of operator theory in complex function spaces.

Abstract

Let $\phi$ be an analytic self-map and $u$ be a fixed analytic function on the open unit disk $D$ in the complex plane $\CC.$ The weighted composition operator is defined\break by \begin{equation*} uC_\phi f =u \cdot (f\circ \phi), f \in H(D). \end{equation*} Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function theoretic properties of their inducing maps.