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

Bourdaud, Gérard

doi:10.5802/aif.1915

Remarques sur certains sous-espaces de

B M O (ℝ^{n})

et de

b m o (ℝ^{n})

Bourdaud, Gérard ¹

¹ Université Paris VII, UFR de Mathématiques, 2 place Jussieu, 75251 Paris Cedex 05 (France)

Annales de l'Institut Fourier, Tome 52 (2002) no. 4, pp. 1187-1218.

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.

MR Zbl

DOI : 10.5802/aif.1915

Classification : 46E30, 42B35
Mot clés : oscillations moyennes bornées, oscillations moyennes continues
Keywords: bounded mean oscillations, vanishing mean oscillations, continuous mean oscillations

Affiliations des auteurs :

Bourdaud, Gérard ¹

¹ Université Paris VII, UFR de Mathématiques, 2 place Jussieu, 75251 Paris Cedex 05 (France)

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     title = {Remarques sur certains sous-espaces de $BMO ({\mathbb {R}}^n)$ et de $bmo({\mathbb {R}}^n)$},
     journal = {Annales de l'Institut Fourier},
     pages = {1187--1218},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     mrnumber = {1927078},
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     url = {http://archive.numdam.org/articles/10.5802/aif.1915/}
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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) no. 4, pp. 1187-1218. doi : 10.5802/aif.1915. http://archive.numdam.org/articles/10.5802/aif.1915/

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