On weak convergence in $H^ 1(\textbf {R}^ d)$
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- by Peter W. Jones and Jean-Lin Journé PDF
- Proc. Amer. Math. Soc. 120 (1994), 137-138 Request permission
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
- R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), no. 2, 249–254. MR 565349, DOI 10.1090/S0002-9939-1980-0565349-8
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 137-138
- MSC: Primary 42B30; Secondary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1994-1159172-3
- MathSciNet review: 1159172