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Holder exponents of arbitrary functions
Ayache A. et al
Revista Matemática Iberoamericana 26, 1 (2010) 77--89 - http://hal-upec-upem.archives-ouvertes.fr/hal-00693033
Antoine Ayache1, Stephane Jaffard2
1:  LPP - Laboratoire Paul Painlevé
http://math.univ-lille1.fr/
CNRS : UMR8524 – Université Lille I - Sciences et technologies
U.F.R. de Mathématiques 59 655 Villeneuve d'Ascq Cédex
France
2:  LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
http://umr-math.univ-mlv.fr/
Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout
Université de Paris-Est - Marne-la-Vallée, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2, Lab Anal & Math Appl, Equipe Anal & Math Appl
France
Mathematics/Mathematical Physics
Holder exponents of arbitrary functions
The functional class of Holder exponents of continuous function has been completely characterized by P. Andersson, K. Daoudi, S. Jaffard, J. Levy Vehel and Y. Meyer [1, 2, 6, 9]; these authors have shown that this class exactly corresponds to that of the lower limits of the sequences of nonnegative continuous functions. The problem of determining whether or not the Holder exponents of discontinuous (and even unbounded) functions can belong to a larger class remained open during the last decade. The main goal of our article is to show that this is not the case: the latter Holder exponents can also be expressed as lower limits of sequences of continuous functions. Our proof mainly relies on a "wavelet-leader" reformulation of a nice characterization of pointwise Holder regularity due to P. Anderson.
English


Revista Matemática Iberoamericana
international
2010
26
1
77--89