Volume 32, Issue 3
Closed Range Composition Operators on a General Family of Function Spaces

Anal. Theory Appl., 32 (2016), pp. 215-231

Published online: 2016-07

Preview Full PDF 271 1197
Export citation

Cited by

• 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.

• Keywords

Composition operators $F(p q s)$ spaces closed range Carleson measure Bloch space Bergman type space