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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Email: cima@math.unc.edu

Alec Matheson
Email: matheson@math.lamar.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-02995-4
PII: S 0002-9939(96)02995-4
Keywords: $H^1$, weak${}^*$ convergence, weak convergence
Communicated by: \commby Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society