Proceedings of the American Mathematical Society

Author(s): Boo Rim Choe; Wade Ramey; David Ullrich
Journal: Proc. Amer. Math. Soc. 125 (1997), 2987-2996.
MSC (1991): Primary 30D45, 47B38
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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.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30D45, 47B38

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

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