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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 | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

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  • [2] C. Fefferman and E. M. Stein, $ {H^p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. MR 0447953 (56:6263)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1159172-3
Keywords: $ {H^1}$, BMO, VMO
Article copyright: © Copyright 1994 American Mathematical Society