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2011 Composition operators acting between some weighted Möbius invariant spaces
M‎. ‎A‎. ‎Bakhit, A‎. ‎El-Sayed Ahmed
Ann. Funct. Anal. 2(2): 138-152 (2011). DOI: 10.15352/afa/1399900202

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 $\phi$‎.

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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

Information

Published: 2011
First available in Project Euclid: 12 May 2014

zbMATH: 1276.47030
MathSciNet: MR2855294
Digital Object Identifier: 10.15352/afa/1399900202

Subjects:
Primary: 47B33
Secondary: ‎46E15

Rights: Copyright © 2011 Tusi Mathematical Research Group

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Vol.2 • No. 2 • 2011
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