Wavelet techniques for pointwise regularity

Stéphane Jaffard

doi:10.5802/afst.1111

Stéphane Jaffard

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 1, pp. 3-33.

Résumé
Abstract

Soit $E$ un espace de Banach (ou un quasi-Banach) invariant par translation et dilatation (typiquement un espace de Besov ou de Sobolev homogène). Nous introduisons une définition générale de régularité ponctuelle associée à $E$ , et notée $C_{E}^{α} (x_{0})$ . Nous montrons comment les propriétés de $E$ se traduisent en propriétés de $C_{E}^{α} (x_{0})$ . Nous donnons également des application en analyse multifractale.

Let $E$ be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with $E$ , and denoted by $C_{E}^{α} (x_{0})$ . We show how properties of $E$ are transferred into properties of $C_{E}^{α} (x_{0})$ . Applications are given in multifractal analysis.

Publié le : 2009-02-26

MR 2225745 | Zbl pre05208247

DOI : https://doi.org/10.5802/afst.1111

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     author = {St\'ephane Jaffard},
     title = {Wavelet techniques for pointwise regularity},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {3--33},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 15},
     number = {1},
     year = {2006},
     doi = {10.5802/afst.1111},
     zbl = {pre05208247},
     mrnumber = {2225745},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2006_6_15_1_3_0/}
}

Stéphane Jaffard. Wavelet techniques for pointwise regularity. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 1, pp. 3-33. doi : 10.5802/afst.1111. https://afst.centre-mersenne.org/item/AFST_2006_6_15_1_3_0/

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