Angular Derivatives
and Compact Composition Operators
on the Hardy and Bergman Spaces
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Barbara D. MacCluer and Joel H. Shapiro |
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Canadian J. Math.
38 (1986), 878--906
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| Abstract: In this paper it is shown that for "normally
weighted" Bergman spaces of the unit disc, a composition
operator is compact if and only if its inducing map has a finite
angular derivative at no point of the unit circle. The
same is true for the Hardy space H^p (0 < p < infinity)
provided the inducing map is univalent. These results are completed
for Hardy space, and unified for Bergman spaces, in my subsequent
paper: The essential norm of a composition operator (Annals
of Mathematics 125 (1987), 375--404), |
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