Reference : Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in ...
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/51497
 Title : Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in T_p^\alpha(x) Language : English Author, co-author : Loosveldt, Laurent [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >] Nicolay, Samuel [Université de Liège - ULg > UR Mathematics > Analyse - Analyse fonctionnelle - Ondelettes] Publication date : 1-Jul-2022 Journal title : Journal of Fourier Analysis and Applications Publisher : Birkhaeuser Volume : 28 Issue/season : 4 Peer reviewed : Yes Audience : International ISSN : 1069-5869 e-ISSN : 1531-5851 Country : United States Keywords : [en] Wavelets ; Multifractal analysis ; · Prevalence ; Pointwise smoothness ; Generalized smoothness Abstract : [en] We present prevalent results concerning generalized versions of the $T_p^\alpha$ spaces, initially introduced by Calderón and Zygmund. We notably show that the logarithmic correction appearing in the quasi-characterization of such spaces is mandatory for almost every function; it is in particular true for the Hölder spaces, for which the existence of the correction was showed necessary for a specific function. We also show that almost every function from $T_p^α (x0 )$ has α as generalized Hölder exponent at $x_0$. Target : Researchers ; Professionals Permalink : http://hdl.handle.net/10993/51497 Other URL : https://link.springer.com/content/pdf/10.1007/s00041-022-09951-5.pdf

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