Date of Graduation
8-2018
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor
Maria Tjani
Committee Member
Phil Harrington
Second Committee Member
Daniel Luecking
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