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

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

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