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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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