TY - JOUR T1 - Closed Range Composition Operators on a General Family of Function Spaces JO - Analysis in Theory and Applications VL - 3 SP - 215 EP - 231 PY - 2016 DA - 2016/07 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n3.2 UR - https://global-sci.org/intro/article_detail/ata/4667.html KW - Composition operators, $F(p,q,s)$ spaces, closed range, Carleson measure, Bloch space, Bergman type space. AB -

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.