Abstract
In this paper we investigate conditions under which a holomorphic self-map of the unit disk induces a composition operator $C_\phi$ with closed range on the weighted Bloch space $\mathcal{B}_{\log}$. Also, we introduce a new class of functions the so called $F_{\log}(p,q,s)$ spaces. Necessary and sufficient conditions are given for a composition operator $C_\phi$ to be bounded and compact from ${\mathcal{B}_{\log}}$ to $F_{\log}(p,q,s)$. Moreover, necessary and sufficient conditions for $C_{\phi}$ from the Dirichlet space $\mathcal{D}$ to the spaces $F_{\log}(p,q,s)$ to be compact are given in terms of the map $\phi$.
Citation
M. A. Bakhit. A. El-Sayed Ahmed. "Composition operators acting between some weighted Möbius invariant spaces." Ann. Funct. Anal. 2 (2) 138 - 152, 2011. https://doi.org/10.15352/afa/1399900202
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