(untitled) (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.