Remarks on some subspaces of B M O ( ℝ n ) and of b m o ( ℝ n )

Gérard Bourdaud[1]

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

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 4, page 1187-1218
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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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 52.4 (2002): 1187-1218. <http://eudml.org/doc/116007>.

@article{Bourdaud2002,
abstract = {On décrit de diverses façons les fermetures respectives, dans l’espace $BMO(\{\mathbb \{R\}\}^n)$ et dans sa version locale $bmo(\{\mathbb \{R\}\}^n)$, 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.},
affiliation = {Université Paris VII, UFR de Mathématiques, 2 place Jussieu, 75251 Paris Cedex 05 (France)},
author = {Bourdaud, Gérard},
journal = {Annales de l’institut Fourier},
keywords = {bounded mean oscillations; vanishing mean oscillations; continuous mean oscillations},
language = {fre},
number = {4},
pages = {1187-1218},
publisher = {Association des Annales de l'Institut Fourier},
title = {Remarques sur certains sous-espaces de $BMO (\{\mathbb \{R\}\}^n)$ et de $bmo(\{\mathbb \{R\}\}^n)$},
url = {http://eudml.org/doc/116007},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Bourdaud, Gérard
TI - Remarques sur certains sous-espaces de $BMO ({\mathbb {R}}^n)$ et de $bmo({\mathbb {R}}^n)$
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 4
SP - 1187
EP - 1218
AB - On décrit de diverses façons les fermetures respectives, dans l’espace $BMO({\mathbb {R}}^n)$ et dans sa version locale $bmo({\mathbb {R}}^n)$, 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.
LA - fre
KW - bounded mean oscillations; vanishing mean oscillations; continuous mean oscillations
UR - http://eudml.org/doc/116007
ER -

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