A wavelet characterization of the pointwise regularity condition 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 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.
Accepted:
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Stéphane Jaffard 1, 2
@article{CRMATH_2004__339_11_757_0, author = {St\'ephane Jaffard}, title = {Pointwise regularity criteria}, journal = {Comptes Rendus. Math\'ematique}, pages = {757--762}, publisher = {Elsevier}, volume = {339}, number = {11}, year = {2004}, doi = {10.1016/j.crma.2004.10.011}, language = {en}, }
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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