Closed Range Composition Operators on a General Family of Function Spaces (Analysis in Theory and Applications, 2016)
In this paper, necessary and sufficient conditions for a closed range composition operator $C_{φ}$ on the general family of holomorphic function spaces $F(p, q, s)$ and more generally on $α$-Besov type spaces $F(p, α p-2, s)$ are given. We give a Carleson measure characterization on $F(p, α p-2, s)$ spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of $C_{φ}$ on $F(p,q,s)$ and $F(p,α p-2,s)$ spaces.
Keywords: Composition operators; $F(p; q; s)$ spaces; closed range; Carleson measure; Bloch space; Bergman type space.