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University of Arkansas

Isometries of Besov Type Spaces among Composition Operators

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 × 2

Identifiers

dc:identifier.*
Repository record dc:identifier
https://scholarworks.uark.edu/etd/1225
OAI identifier oai:identifier
oai:scholarworks.uark.edu:etd-2224

Chain of custody

source
Harvested from
University of Arkansas
Base URL
scholarworks.uark.edu/do/oai/
Last updated
2026-07-24
Source record
OAI-PMH GetRecord
citation

Shabazz, Melissa Ann. Isometries of Besov Type Spaces among Composition Operators. Dissertation thesis, 2015. https://scholarworks.uark.edu/etd/1225