Bloch-to-BMOA pullbacks on the disk

Authors:
Boo Rim Choe, Wade Ramey and David Ullrich

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2987-2996

MSC (1991):
Primary 30D45, 47B38

DOI:
https://doi.org/10.1090/S0002-9939-97-03873-2

MathSciNet review:
1396971

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Abstract | References | Similar Articles | Additional Information

Abstract: For a given holomorphic self map of the unit disk, we consider the Bloch-to- composition property (pullback property) of . Our results are cannot have the pullback property if touches the boundary too smoothly, while has the pullback property if touches the boundary rather sharply. One of these results yields an interesting consequence completely contrary to a higher dimensional result which has been known. These results resemble known results concerning the compactness of composition operators on the Hardy spaces. Some remarks in that direction are included.

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Additional Information

**Boo Rim Choe**

Affiliation:
Department of Mathematics, Korea University, Seoul, Korea

Email:
choebr@semi.korea.ac.kr

**Wade Ramey**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan

Email:
ramey@math.msu.edu

**David Ullrich**

Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma

Email:
ullrich@hardy.math.okstate.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03873-2

Keywords:
Bloch space,
BMOA,
pullback property

Received by editor(s):
September 22, 1995

Received by editor(s) in revised form:
May 17, 1996

Additional Notes:
The first author is supported in part by BSRI (96-1407) and GARC (96) of Korea.

Communicated by:
Theodore Gamelin

Article copyright:
© Copyright 1997
American Mathematical Society