On weak* convergence in 𝐻¹

Cima, Joseph; Matheson, Alec

doi:10.1090/S0002-9939-96-02995-4

On weak${}^*$ convergence in $H^1$
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by Joseph A. Cima and Alec Matheson

Proc. Amer. Math. Soc. 124 (1996), 161-163

DOI: https://doi.org/10.1090/S0002-9939-96-02995-4

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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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