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Local VMO and Weak Convergence in h1

Published online by Cambridge University Press:  20 November 2018

Galia Dafni
Galia Dafni*
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. W., Montréal, Québec, H3G 1M8, email: gdafni@discrete.concordia.ca
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Abstract

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A local version of $\text{VMO}$ is defined, and the local Hardy space ${{h}_{1}}$ is shown to be its dual. An application to weak-$*$ convergence in ${{h}_{1}}$ is proved.

Keywords

42B3046E99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 46 - 59
Copyright
Copyright © Canadian Mathematical Society 2002

References

[Ch] Chang, D.-C., The dual of Hardy spaces on a bounded domain in Rn. ForumMath. 6 (1994), 65–81.Google Scholar
[CLMS] Coifman, R., Lions, P.-L., Meyer, Y. and Semmes, S., Compensated compactness and Hardy spaces. J. Math. Pures Appl. (9) 72(1993), no. 3, 247–286.Google Scholar
[CR] Coifman, R. R. and Rochberg, R., Another Characterization of BMO. Proc. Amer. Math. Soc. 79 (1980), 249–254.Google Scholar
[CW] Coifman, R. R. and Weiss, G., Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), 569–645.Google Scholar
[F] Fefferman, C., Characterizations of bounded mean oscillation. Bull. Amer. Math. Soc. 77 (1971), 587–588.Google Scholar
[FS] Fefferman, C. and Stein, E. M., Hp spaces of several variables. Acta Math. 129 (1972), 137–193.Google Scholar
[GCRdF] García-Cuerva, J. and de Francia, J. L. Rubio, Weighted Norm Inequalities and Related Topics. North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985.Google Scholar
[Ga] Garnett, J. B., Bounded analytic functions. Pure Appl. Math. 96, Academic Press, New York-London, 1981.Google Scholar
[G] Goldberg, D., A local version of real Hardy spaces. DukeMath. J. 46 (1979), 27–42.Google Scholar
[JJ] Jones, P. W. and Journé, J.-L., On Weak Convergence in H1(Rd). Proc. Amer.Math. Soc. 120 (1994), 137–138.Google Scholar
[Sa] Sarason, D., Functions of vanishing mean oscillation. Trans. Amer.Math. Soc. 207 (1975), 391–405.Google Scholar
[S] Stein, E. M., Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 1970.Google Scholar