Weighted Composition Operators from the Besov Spaces into the Bloch Spaces

Flavia Colonna ; Songxiao Li

Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 4

Résumé

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.

Détail

Classification : Primary: 47B33, Secondary: 30H30