Remarques sur certains sous-espaces de BMO( n ) et de bmo( n )
Annales de l'Institut Fourier, Tome 52 (2002) no. 4, pp. 1187-1218.

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.

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.

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 $$ et de $$},
     journal = {Annales de l'Institut Fourier},
     pages = {1187--1218},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {4},
     year = {2002},
     doi = {10.5802/aif.1915},
     zbl = {1061.46025},
     mrnumber = {1927078},
     language = {fr},
     url = {aif.centre-mersenne.org/item/AIF_2002__52_4_1187_0/}
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Bourdaud, Gérard. Remarques sur certains sous-espaces de $$ et de $$. Annales de l'Institut Fourier, Tome 52 (2002) no. 4, pp. 1187-1218. doi : 10.5802/aif.1915. https://aif.centre-mersenne.org/item/AIF_2002__52_4_1187_0/

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