Holder exponents of arbitrary functions
Document type :
Article dans une revue scientifique: Article original
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Title :
Holder exponents of arbitrary functions
Author(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]
Journal title :
Revista Matemática Iberoamericana
Pages :
77--89
Publisher :
European Mathematical Society
Publication date :
2010
ISSN :
0213-2230
HAL domain(s) :
Mathématiques [math]/Physique mathématique [math-ph]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Submission date :
2025-01-24T10:34:38Z