Holder exponents of arbitrary functions
Type de document :
Article dans une revue scientifique: Article original
URL permanente :
Titre :
Holder exponents of arbitrary functions
Auteur(s) :
Ayache, Antoine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Jaffard, Stephane [Auteur]
Laboratoire d'Analyse et de Mathématiques Appliquées [LAMA]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Jaffard, Stephane [Auteur]
Laboratoire d'Analyse et de Mathématiques Appliquées [LAMA]
Titre de la revue :
Revista Matemática Iberoamericana
Pagination :
77--89
Éditeur :
European Mathematical Society
Date de publication :
2010
ISSN :
0213-2230
Discipline(s) HAL :
Mathématiques [math]/Physique mathématique [math-ph]
Résumé en anglais : [en]
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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Collections :
Source :
Date de dépôt :
2025-01-24T10:34:38Z