Comptes Rendus
Mathematical Analysis/Harmonic Analysis
Pointwise regularity criteria
Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 757-762.

A wavelet characterization of the pointwise regularity condition Tup(x0) of Calderón and Zygmund is obtained. The extremal case (a pointwise BMO condition) yields the sharpest wavelet condition which is implied by pointwise Hölder regularity; in particular, this criterium is sharper than the usual two-microlocal condition.

On obtient une caractérisation par ondelettes de la condition de régularité ponctuelle Tup(x0) de Calderón et Zygmund. Le cas extrème (une condition de type BMO local) fournit la condition la plus précise sur les modules des coefficients d'ondelette impliquée par la régularité Hölderienne ponctuelle ; en particulier elle est plus fine que le critère deux-microlocal usuel.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.10.011

Stéphane Jaffard 1, 2

1 Laboratoire d'analyse et de mathématiques appliquées, université Paris XII, 61, avenue du Général de Gaulle, 94010 Créteil cedex, France
2 Institut universitaire de France, 103, boulevard Saint-Michel 75005 Paris, France
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     title = {Pointwise regularity criteria},
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Stéphane Jaffard. Pointwise regularity criteria. Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 757-762. doi : 10.1016/j.crma.2004.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.011/

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