Abstract
dc:description.abstract<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>
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy in Mathematics (PhD)
- Level thesis:degree_level
- Dissertation
- Year dc:date.available
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Shabazz, Melissa Ann
- Advisor dc:contributor.advisor
-
- Tjani, Maria
- Contributors dc:contributor
-
- Akeroyd, John R.
- Luecking, Daniel H.
Subjects
dc:subject × 2Identifiers
dc:identifier.*- Repository record dc:identifier
- https://scholarworks.uark.edu/etd/1225
- OAI identifier oai:identifier
- oai:scholarworks.uark.edu:etd-2224