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Wavelet techniques for pointwise regularity
Stéphane Jaffard1
1Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris XII, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex (France).
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.

Published online:
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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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

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