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, ∞).
","abstract_html":"<p>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,∞). </p> <p>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, ∞). </p>","abstract_has_math":false,"creators":["Erdem, Kevser"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematics (PhD)","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Harrington, Phillip S.","Luecking, Daniel H."],"advisors":["Tjani, Maria"],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-08-01T07:00:00Z","date_published":"2018-08-01T07:00:00Z","updated_at":"2026-07-24T01:00:28Z","subjects":["BMOA","Closed Range Composition Operators","Counting Functions","Reverse Carleson Conditions","Sampling Sets","Numerical Analysis and Computation"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/2831","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Harrington, Phillip S.","Luecking, Daniel H."]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Tjani, Maria"]},{"key":"dc:creator","label":"Author","values":["Erdem, Kevser"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-02-06T08:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy in Mathematics (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["BMOA","Closed Range Composition Operators","Counting Functions","Reverse Carleson Conditions","Sampling Sets","Numerical Analysis and Computation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/2831"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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, ∞).
"]},{"key":"dc:title","label":"Title","values":["Closed Range Composition Operators on BMOA"]}]}],"canonical_facts":{"dc:contributor":["Harrington, Phillip S.","Luecking, Daniel H."],"dc:contributor.advisor":["Tjani, Maria"],"dc:creator":["Erdem, Kevser"],"dc:date":["2018"],"dc:date.available":["2024-02-06T08:00:00Z"],"dc:description.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, ∞).
"],"dc:identifier":["https://scholarworks.uark.edu/etd/2831"],"dc:subject":["BMOA","Closed Range Composition Operators","Counting Functions","Reverse Carleson Conditions","Sampling Sets","Numerical Analysis and Computation"],"dc:title":["Closed Range Composition Operators on BMOA"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy in Mathematics (PhD)"]},"updated_at":"2026-07-24T01:00:28Z"}