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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\sp 1({\bf R}\sp d)$


Authors: Peter W. Jones and Jean-Lin Journé
Journal: Proc. Amer. Math. Soc. 120 (1994), 137-138
MSC: Primary 42B30; Secondary 30D55
MathSciNet review: 1159172
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Abstract: We prove that the a.e. convergence of a sequence of functions bounded in $ {H^1}({{\mathbf{R}}^d})$ to a function in $ {L^1}({{\mathbf{R}}^d})$ implies weak convergence.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1159172-3
PII: S 0002-9939(1994)1159172-3
Keywords: $ {H^1}$, BMO, VMO
Article copyright: © Copyright 1994 American Mathematical Society