Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Maria Tjani Committee members: Phil Harrington; Daniel Luecking.
Özet:
Let ϕ be an analytic self-map of the unit disk D. The composition operator with symbol ϕ is denoted by Cϕ. Reverse Carleson type conditions, counting functions and sampling sets are important tools to give a complete characterization of closed range composition operators on BMOA and on Qp for all p epsilon (0,infinity).
Let ss denote the Bloch space, let H 2 denote the Hardy space. We show that if Cϕ is closed range on ss or on H2 then it is also closed range on BMOA. Closed range composition operators Cϕ : ss → BMOA are also characterized. Laitila found the isometries among composition operators on BMOA. We extend this to Qp for all p epsilon (0, infinity).