Bulletin

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Volume 36 • Number 4 • 2013

• Weighted Composition Operators from the Besov Spaces into the Bloch Spaces
Flavia Colonna and Songxiao Li

Abstract.
Let

$\varphi$ be an analytic self-map of the open unit disk

$\mathbb{D}$ in the complex plane

$\mathbb{C}$ and let

$u$ be a fixed analytic function on

$\mathbb{D}$ . The weighted composition operator is defined on the space

$H(\mathbb{D})$ of analytic functions on

$\mathbb{D}$ by

$uC_\varphi f =u \cdot (f\circ \varphi), \ \ f \in H(\mathbb{D})$ . In this work, we characterize the bounded and the compact weighted composition operators from the Besov spaces

$B_{p}$ (1<

$p$ >\infty) into the Bloch space as well as into the little Bloch space.

2010 Mathematics Subject Classification: Primary: 47B33, Secondary: 30H30

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