Composition operators on some holomorphic Banach function spaces - El-Sayed Ahmed, A.; Bakhit, M.A. (MATHEMATICA SCANDINAVICA, 2009)
In this paper, we study composition operators on some Möbius invariant Banach function spaces like Bloch and F(p,q,s) spaces. We give a Carleson measure characterization on F(p,q,s) spaces, then we use this Carleson measure characterization of the compact compositions on F(p,q,s) spaces to show that every compact composition operator on F(p,q,s) spaces is compact on a Bloch space. Also, we give conditions to clarify when the converse holds.