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, ∞).

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