Date of Graduation
8-2018
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
Tjani, Maria
Committee Member
Harrington, Phillip S.
Second Committee Member
Luecking, Daniel H.
Keywords
BMOA; Closed Range Composition Operators; Counting Functions; Reverse Carleson Conditions; Sampling Sets
Abstract
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 ∈ (0,∞).
Let B denote the Bloch space, let H2 denote the Hardy space. We show that if Cφ is closed range on B or on H2 then it is also closed range on BMOA. Closed range composition operators Cφ : B → BMOA are also characterized. Laitila found the isometries among composition operators on BMOA. We extend this to Qp for all p ∈ (0, ∞).
Citation
Erdem, K. (2018). Closed Range Composition Operators on BMOA. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/2831
