Year: 2016
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 3 : pp. 215–231
Abstract
In this paper, necessary and sufficient conditions for a closed range composition operator $C_{\phi}$ on the general family of holomorphic function spaces $F(p, q, s)$ and more generally on $\alpha$-Besov type spaces $F(p, \alpha p-2, s)$ are given. We give a Carleson measure characterization on $F(p, \alpha p-2, s)$ spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of $C_{\phi}$ on $F(p,q,s)$ and $F(p,\alpha p-2,s)$ spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n3.2
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 3 : pp. 215–231
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Composition operators $F(p q s)$ spaces closed range Carleson measure Bloch space Bergman type space.