Let 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 , and denoted by . We show how properties of are transferred into properties of . Applications are given in multifractal analysis.
Soit 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 , et notée . Nous montrons comment les propriétés de se traduisent en propriétés de . 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}, pages = {3--33}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 15}, number = {1}, year = {2006}, doi = {10.5802/afst.1111}, mrnumber = {2225745}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1111/} }
TY - JOUR AU - Jaffard, Stéphane TI - Wavelet techniques for pointwise regularity JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2006 SP - 3 EP - 33 VL - 15 IS - 1 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1111/ DO - 10.5802/afst.1111 LA - en ID - AFST_2006_6_15_1_3_0 ER -
%0 Journal Article %A Jaffard, Stéphane %T Wavelet techniques for pointwise regularity %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2006 %P 3-33 %V 15 %N 1 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1111/ %R 10.5802/afst.1111 %G en %F 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://archive.numdam.org/articles/10.5802/afst.1111/
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