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 and in its local version , 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 et dans sa version locale , de l’ensemble des fonctions à support compact et de l’ensemble des fonctions 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.
Mot clés : oscillations moyennes bornées, oscillations moyennes continues
Keywords: bounded mean oscillations, vanishing mean oscillations, continuous mean oscillations
Bourdaud, Gérard 1
@article{AIF_2002__52_4_1187_0, 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}, pages = {1187--1218}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {4}, year = {2002}, doi = {10.5802/aif.1915}, zbl = {1061.46025}, mrnumber = {1927078}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1915/} }
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 SP - 1187 EP - 1218 VL - 52 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1915/ DO - 10.5802/aif.1915 LA - fr ID - AIF_2002__52_4_1187_0 ER -
%0 Journal Article %A Bourdaud, Gérard %T Remarques sur certains sous-espaces de $BMO ({\mathbb {R}}^n)$ et de $bmo({\mathbb {R}}^n)$ %J Annales de l'Institut Fourier %D 2002 %P 1187-1218 %V 52 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1915/ %R 10.5802/aif.1915 %G fr %F 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, 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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