Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces $C^{α}_{E}(x₀)$ are constructed, leading to a notion of pointwise regularity with respect to E; the case $E = L^{∞}$ corresponds to the usual Hölder regularity, and $E = L^{p}$ corresponds to the $T^{p}_{α}(x₀)$ regularity of Calderón and Zygmund. We focus on the study of the spaces $T^{p}_{α}(x₀)$; in particular, we give their characterization in terms of a wavelet basis and show their invariance under standard pseudodifferential operators of order 0.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
93-100
Opis fizyczny
Daty
wydano
2006
Twórcy
autor
- Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris XII, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-7