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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compact composition operators
on the Nevanlinna class


Authors: Jun Soo Choa and Hong Oh Kim
Journal: Proc. Amer. Math. Soc. 125 (1997), 145-151
MSC (1991): Primary 47B05, 47B38; Secondary 30D55
MathSciNet review: 1346966
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Abstract: In this paper we prove that the composition operator induced by a holomorphic self-map of the unit disc is compact on the Nevanlinna class if and only if it is compact on the Hardy space $H^2$.


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Additional Information

Jun Soo Choa
Affiliation: Department of Mathematics Education, Sung Kyun Kwan University, Jongro-Gu, Seoul 110-745, Korea
Email: jschoa@yurim.skku.ac.kr

Hong Oh Kim
Affiliation: Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Yusung-gu Gusung-dong, Taejun 305-701, Korea

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03534-X
PII: S 0002-9939(97)03534-X
Keywords: Compact composition operator, Nevanlinna counting function, Carleson measure
Received by editor(s): May 2, 1995
Received by editor(s) in revised form: June 30, 1995
Additional Notes: Supported in part by TGRC, and Korean ministry of Education, BSRI-95-1420
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society