Proceedings of the American Mathematical Society

Author(s): Joseph A. Cima; Alec Matheson
Journal: Proc. Amer. Math. Soc. 124 (1996), 161-163.
MSC (1991): Primary 42B30; Secondary 30D55
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42B30, 30D55

Joseph A. Cima
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
Email: cima@math.unc.edu

Alec Matheson
Affiliation: Department of Mathematics, Lamar University, Beaumont, Texas 77710
Email: matheson@math.lamar.edu

DOI: 10.1090/S0002-9939-96-02995-4
PII: S 0002-9939(96)02995-4
Keywords: $H^1$, weak${}^*$ convergence, weak convergence
Communicated by: Dale Alspach
Copyright of article: Copyright 1996, American Mathematical Society

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