Weighted composition operators from Bergman-type spaces into Bloch spaces

Details Weighted composition operators from Bergman-type spaces into Bloch spaces Weighted composition operators from Bergman-type spaces into Bloch spaces

2007-09-21

arxiv.org/abs/0709.3347v1

Mathematics

Complex Variables

15 pages

Scientific paper

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.

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