Local VMO and Weak Convergence in h 1
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 46-59

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2002-005-2
Mots-clés : 42B30, 46E99
Dafni, Galia. Local VMO and Weak Convergence in h 1. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 46-59. doi: 10.4153/CMB-2002-005-2
@article{10_4153_CMB_2002_005_2,
     author = {Dafni, Galia},
     title = {Local {VMO} and {Weak} {Convergence} in h 1},
     journal = {Canadian mathematical bulletin},
     pages = {46--59},
     year = {2002},
     volume = {45},
     number = {1},
     doi = {10.4153/CMB-2002-005-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-005-2/}
}
TY  - JOUR
AU  - Dafni, Galia
TI  - Local VMO and Weak Convergence in h 1
JO  - Canadian mathematical bulletin
PY  - 2002
SP  - 46
EP  - 59
VL  - 45
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-005-2/
DO  - 10.4153/CMB-2002-005-2
ID  - 10_4153_CMB_2002_005_2
ER  - 
%0 Journal Article
%A Dafni, Galia
%T Local VMO and Weak Convergence in h 1
%J Canadian mathematical bulletin
%D 2002
%P 46-59
%V 45
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-005-2/
%R 10.4153/CMB-2002-005-2
%F 10_4153_CMB_2002_005_2

[Ch] [Ch] Chang, D.-C., The dual of Hardy spaces on a bounded domain in Rn. ForumMath. 6 (1994), 65–81. Google Scholar

[CLMS] [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] [CR] Coifman, R. R. and Rochberg, R., Another Characterization of BMO. Proc. Amer. Math. Soc. 79 (1980), 249–254. Google Scholar

[CW] [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] [F] Fefferman, C., Characterizations of bounded mean oscillation. Bull. Amer. Math. Soc. 77 (1971), 587–588. Google Scholar

[FS] [FS] Fefferman, C. and Stein, E. M., H spaces of several variables. Acta Math. 129 (1972), 137–193. Google Scholar

[GCRdF] [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] [Ga] Garnett, J. B., Bounded analytic functions. Pure Appl. Math. 96, Academic Press, New York-London, 1981. Google Scholar

[G] [G] Goldberg, D., A local version of real Hardy spaces. DukeMath. J. 46 (1979), 27–42. Google Scholar

[JJ] [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] [Sa] Sarason, D., Functions of vanishing mean oscillation. Trans. Amer.Math. Soc. 207 (1975), 391–405. Google Scholar

[S] [S] Stein, E. M., Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 1970. Google Scholar

Cité par Sources :