Remarques sur certains sous-espaces de $BMO ({\mathbb {R}}^n)$ et de $bmo({\mathbb {R}}^n)$

Bourdaud, Gérard

Remarques sur certains sous-espaces de

B M O (ℝ^{n})

et de

b m o (ℝ^{n})

Bourdaud, Gérard

Annales de l'Institut Fourier, Tome 52 (2002), p. 1187-1218 / Harvested from Numdam

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Résumé
Abstract

On décrit de diverses façons les fermetures respectives, dans l’espace $B M O (ℝ^{n})$ et dans sa version locale $b m o (ℝ^{n})$ , 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.

We present various characterizations of the closure of the set of functions with compact support and of the set of infinitely differentiable functions with compact support in the space $B M O (ℝ^{n})$ and in its local version $b m o (ℝ^{n})$ , respectively. Some of these results are novel, some others are considered as classical, although an explicit proof does not seem to have been published. By means of counterexamples, we show the differences among the various subspaces we have considered.

Publié le : 2002-01-01

MR 1927078 | Zbl 1061.46025

DOI : https://doi.org/10.5802/aif.1915
Classification: 46E30, 42B35
Mots clés: oscillations moyennes bornées, oscillations moyennes continues

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     author = {Bourdaud, G\'erard},
     title = {Remarques sur certains sous-espaces de $BMO ({\mathbb {R}}^n)$ et de $bmo({\mathbb {R}}^n)$},
     journal = {Annales de l'Institut Fourier},
     volume = {52},
     year = {2002},
     pages = {1187-1218},
     doi = {10.5802/aif.1915},
     mrnumber = {1927078},
     zbl = {1061.46025},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2002__52_4_1187_0}
}

Bourdaud, Gérard. Remarques sur certains sous-espaces de $BMO ({\mathbb {R}}^n)$ et de $bmo({\mathbb {R}}^n)$. Annales de l'Institut Fourier, Tome 52 (2002) pp. 1187-1218. doi : 10.5802/aif.1915. http://gdmltest.u-ga.fr/item/AIF_2002__52_4_1187_0/

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