Bloch-to-BMOA pullbacks on the disk
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- by Boo Rim Choe, Wade Ramey and David Ullrich
- Proc. Amer. Math. Soc. 125 (1997), 2987-2996
- DOI: https://doi.org/10.1090/S0002-9939-97-03873-2
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Abstract:
For a given holomorphic self map $\varphi$ of the unit disk, we consider the Bloch-to-$BMOA$ composition property (pullback property) of $\varphi$. Our results are $(1)$ $\varphi$ cannot have the pullback property if $\varphi$ touches the boundary too smoothly, $(2)$ while $\varphi$ has the pullback property if $\varphi$ 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.References
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Bibliographic Information
- Boo Rim Choe
- Affiliation: Department of Mathematics, Korea University, Seoul, Korea
- MR Author ID: 251281
- 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
- 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
- © Copyright 1997 American Mathematical Society
- 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