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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

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

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