Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by Martin, Vukotic and by Allen, Heller and Pons on certain Besov spaces.
","abstract_html":"<p>Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by Martin, Vukotic and by Allen, Heller and Pons on certain Besov spaces.</p>","abstract_has_math":false,"creators":["Shabazz, Melissa Ann"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematics (PhD)","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Akeroyd, John R.","Luecking, Daniel H."],"advisors":["Tjani, Maria"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-07-01T07:00:00Z","date_published":"2015-07-01T07:00:00Z","updated_at":"2026-07-24T00:58:53Z","subjects":["Pure sciences","Other Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/1225","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Akeroyd, John R.","Luecking, Daniel H."]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Tjani, Maria"]},{"key":"dc:creator","label":"Author","values":["Shabazz, Melissa Ann"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-09-29T07:00:00Z"]},{"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":["Pure sciences","Other Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/1225"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by Martin, Vukotic and by Allen, Heller and Pons on certain Besov spaces.
"]},{"key":"dc:title","label":"Title","values":["Isometries of Besov Type Spaces among Composition Operators"]}]}],"canonical_facts":{"dc:contributor":["Akeroyd, John R.","Luecking, Daniel H."],"dc:contributor.advisor":["Tjani, Maria"],"dc:creator":["Shabazz, Melissa Ann"],"dc:date":["2015"],"dc:date.available":["2017-09-29T07:00:00Z"],"dc:description.abstract":["Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by Martin, Vukotic and by Allen, Heller and Pons on certain Besov spaces.
"],"dc:identifier":["https://scholarworks.uark.edu/etd/1225"],"dc:subject":["Pure sciences","Other Applied Mathematics"],"dc:title":["Isometries of Besov Type Spaces among Composition Operators"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy in Mathematics (PhD)"]},"updated_at":"2026-07-24T00:58:53Z"}