Date of Graduation
7-2015
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
Tjani, Maria
Committee Member
Akeroyd, John R.
Second Committee Member
Luecking, Daniel H.
Keywords
Pure sciences
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.
Citation
Shabazz, M. A. (2015). Isometries of Besov Type Spaces among Composition Operators. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/1225
