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Transactions of the American Mathematical Society

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Compact composition operators on Besov spaces

Author: Maria Tjani
Journal: Trans. Amer. Math. Soc. 355 (2003), 4683-4698
MSC (2000): Primary 47B38; Secondary 30D45, 46E15
Published electronically: July 8, 2003
MathSciNet review: 1990767
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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.

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Additional Information

Maria Tjani
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701

Received by editor(s): June 21, 1999
Received by editor(s) in revised form: March 26, 2003
Published electronically: July 8, 2003
Article copyright: © Copyright 2003 American Mathematical Society