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Gérard Bourdaud
Remarques sur certains sous-espaces de $BMO ({\Bbb R}^n)$ et de $bmo({\Bbb R}^n)$
(Remarks on some subspaces of $BMO ({\Bbb R}^n)$ and of $bmo({\Bbb R}^n)$)
Annales de l'institut Fourier, 52 no. 4 (2002), p. 1187-1218, doi: 10.5802/aif.1915
Article PDF | Analyses MR 1927078 | Zbl 1061.46025
Class. Math.: 46E30, 42B35
Mots clés: oscillations moyennes bornées, oscillations moyennes continues

Résumé - Abstract

On décrit de diverses façons les fermetures respectives, dans l'espace $BMO({\Bbb R}^n)$ et dans sa version locale $bmo({\Bbb R}^n)$, de l'ensemble des fonctions à support compact et de l'ensemble des fonctions $C^\infty$ à support compact. Certains de ces résultats sont nouveaux; d'autres, considérés comme classiques, ne semblent pas avoir fait l'objet de publication. Des contre-exemples permettent de vérifier la diversité des sous-espaces considérés.

Bibliographie

[1] J.M. Angeletti, S. Mazet & Ph. Tchamitchian, Analysis of second order elliptic operators whitout boundary conditions and with VMO or Hölderian coefficients, Academic Press, 1997, p. 495-539
[2] G. Bourdaud, Analyse fonctionnelle dans l'espace Euclidien, Pub. Math. Univ. Paris 7, 1995  Zbl 0627.46048
[3] G. Bourdaud, M. Lanza, de Cristoforis & W. Sickel, “Functional calculus on BMO and related spaces”, J. Funct. Anal. 189 (2002), p. 515-538 Article |  MR 1892179 |  Zbl 1007.47028
[4] D.C. Chang, “The dual of Hardy spaces on a bounded domain in $\scriptstyle\mathbb R^n$”, Forum Math 6 (1994), p. 65-81 Article |  MR 1253178 |  Zbl 0803.42014
[5] R. Coifman, R. Rochberg & G. Weiss, “Factorization theorems for Hardy spaces in several variables”, Ann. of Math 103 (1976), p. 611-635 Article |  MR 412721 |  Zbl 0326.32011
[6] R. Coifman & G. Weiss, “Extension of Hardy spaces and their use in analysis”, Bull. Amer. Math. Soc 83 (1977), p. 569-645 Article |  MR 447954 |  Zbl 0358.30023
[7] C. Fefferman & E.M. Stein, “$H^p$ spaces of several variables”, Acta Math 129 (1972), p. 137-193 Article |  MR 447953 |  Zbl 0257.46078
[8] J.B. Garnett & P.W. Jones, “The distance in $BMO$ to $L^\infty$”, Ann. of Math 108 (1978), p. 373-393 Article |  MR 506992 |  Zbl 0383.26010
[9] D. Goldberg, “A local version of real Hardy space”, Duke Math. J 46 (1979), p. 27-42 Article |  MR 523600 |  Zbl 0409.46060
[10] T. Iwaniec & C. Sbordone, “Riesz transforms and elliptic PDEs with $VMO$ coefficients”, J. Anal. Math 74 (1998), p. 183-212 Article |  MR 1631658 |  Zbl 0909.35039
[11] S. Janson, “On functions with conditions on mean oscillation”, Ark. Mat 14 (1976), p. 189-196 Article |  MR 438030 |  Zbl 0341.43005
[12] F. John & L. Nirenberg, “On functions of bounded mean oscillation”, Comm. Pure Appl. Math 14 (1961), p. 415-426 Article |  MR 131498 |  Zbl 0102.04302
[13] P.W. Jones, “Extension theorems for $BMO$”, Indiana Univ. Math. J 29 (1980), p. 41-66 Article |  MR 554817 |  Zbl 0432.42017
[14] J.D. Lakey, “Constructive decomposition of functions of finite central mean oscillation”, Proc. Amer. Math. Soc 127 (1999), p. 2375-2384 Article |  MR 1486741 |  Zbl 0922.42008
[15] J. Marschall, “Pseudo-differential operators with non-regular symbols”, Thèse FU Berlin, 1985  Zbl 0695.47047
[16] U. Neri, “Fractional integration on the space $H^1$ and its dual”, Studia Math 53 (1975), p. 175-189 Article |  MR 388074 |  Zbl 0269.44012
[17] W. Rudin, Analyse réelle et complexe, Masson, Paris, 1975  MR 662565 |  Zbl 0333.28001
[18] T. Runst & W. Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, De Gruyter, 1996  MR 1419319 |  Zbl 0873.35001
[19] D. Sarason, “Functions of vanishing mean oscillation”, Trans. Amer. Math. Soc 207 (1975), p. 391-405 Article |  MR 377518 |  Zbl 0319.42006
[20] D.A. Stegenga, “Bounded Toeplitz operators on $H^1$ and applications of duality between $H^1$ and the functions of bounded mean oscillation”, Amer. J. Math 98 (1976), p. 573-589 Article |  MR 420326 |  Zbl 0335.47018
[21] E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, Princeton, 1993  MR 1232192 |  Zbl 0821.42001
[22] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986  MR 869816 |  Zbl 0621.42001
[23] A. Uchiyama, “On the compactness of operators of Hankel type”, Tôhoku Math. J 30 (1978), p. 163-171 Article |  MR 467384 |  Zbl 0384.47023
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