Compact composition operators on Besov spaces
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Abstract:
We give a Carleson measure characterization of the compact composition operators on Besov spaces. We use this characterization to show that every compact composition operator on a Besov space is compact on the Bloch space. Finally we give conditions that guarantee that the converse holds.References
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Additional Information
- Maria Tjani
- Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 666446
- Email: mtjani@comp.uark.edu
- Received by editor(s): June 21, 1999
- Received by editor(s) in revised form: March 26, 2003
- Published electronically: July 8, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 4683-4698
- MSC (2000): Primary 47B38; Secondary 30D45, 46E15
- DOI: https://doi.org/10.1090/S0002-9947-03-03354-3
- MathSciNet review: 1990767