Remarques sur certains sous-espaces de BMO( n ) et de bmo( n )
[Remarks on some subspaces of BMO( n ) and of bmo( n )]
Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1187-1218.

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 BMO( n ) and in its local version bmo( 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.

On décrit de diverses façons les fermetures respectives, dans l’espace BMO( n ) et dans sa version locale bmo( n ), de l’ensemble des fonctions à support compact et de l’ensemble des fonctions C 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.

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

Bourdaud, Gérard 1

1 Université Paris VII, UFR de Mathématiques, 2 place Jussieu, 75251 Paris Cedex 05 (France)
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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, Volume 52 (2002) no. 4, pp. 1187-1218. doi : 10.5802/aif.1915. https://aif.centre-mersenne.org/articles/10.5802/aif.1915/

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