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Wavelet techniques for pointwise regularity
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 1, pp. 3-33.

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.

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.

DOI: 10.5802/afst.1111
Stéphane Jaffard 1

1 Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris XII, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex (France).
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     title = {Wavelet techniques for pointwise regularity},
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Stéphane Jaffard. Wavelet techniques for pointwise regularity. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 1, pp. 3-33. doi : 10.5802/afst.1111. https://afst.centre-mersenne.org/articles/10.5802/afst.1111/

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