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On weak${}^*$ convergence in $H^1$

Authors: Joseph A. Cima and Alec Matheson
Journal: Proc. Amer. Math. Soc. 124 (1996), 161-163
MSC (1991): Primary 42B30; Secondary 30D55
MathSciNet review: 1285983
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Abstract: A bounded sequence of functions in $H^1$ which converges in measure on a set of positive measure of the unit circle converges weak${}^*$. An example is given to show that weak${}^*$ convergence cannot be replaced by weak convergence.

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Additional Information

Joseph A. Cima

Alec Matheson

Keywords: $H^1$, weak${}^*$ convergence, weak convergence
Communicated by: \commby Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society

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