Date of Graduation

8-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

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, ∞).

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