Pointwise regularity associated with function spaces and multifractal analysis

• Autorzy: Stéphane Jaffard
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 26A30: Singular functions, Cantor functions, functions with other special properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 72
• Numer: 1
• Strony: 93-100

Daty

wydano

2006

Twórcy

autor

Stéphane Jaffard

• Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris XII, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France

Identyfikatory

DOI

10.4064/bc72-0-7