Carleson measures and some classes

of meromorphic functions

Authors:
Rauno Aulaskari, Hasi Wulan and Ruhan Zhao

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2329-2335

MSC (1991):
Primary 30D50

DOI:
https://doi.org/10.1090/S0002-9939-99-05273-9

Published electronically:
December 7, 1999

MathSciNet review:
1657750

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For let be the Möbius transformation defined by , and let be the Green's function of the unit disk . We construct an analytic function belonging to for all , , but not belonging to meromorphic in and for any , . This gives a clear difference as compared to the analytic case where the corresponding function spaces ( and ) are same.

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Additional Information

**Rauno Aulaskari**

Affiliation:
Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland

Email:
Rauno.Aulaskari@joensuu.fi, wulan@cc.joensuu.fi

**Hasi Wulan**

Affiliation:
Department of Mathematics, Inner Mongolia Normal University, Hohhot 010022, People’s Republic of China

**Ruhan Zhao**

Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

Email:
zhao@kusm.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-99-05273-9

Keywords:
Carleson measure,
normal function,
the $Q_{p}$ space

Received by editor(s):
April 20, 1998

Received by editor(s) in revised form:
September 15, 1998

Published electronically:
December 7, 1999

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 2000
American Mathematical Society