Weighted composition operators from Bergman-type 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 $$ uC_\phi f = u \cdot (f \circ \phi ), f \in H(D). $$ Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function theoretic properties of their inducing maps.