Reference : Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in ...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/51497
Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in T_p^\alpha(x)
English
Loosveldt, Laurent mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Nicolay, Samuel mailto [Université de Liège - ULg > UR Mathematics > Analyse - Analyse fonctionnelle - Ondelettes]
1-Jul-2022
Journal of Fourier Analysis and Applications
Birkhaeuser
28
4
Yes
International
1069-5869
1531-5851
United States
[en] Wavelets ; Multifractal analysis ; · Prevalence ; Pointwise smoothness ; Generalized smoothness
[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 $x_0$.
Researchers ; Professionals
http://hdl.handle.net/10993/51497
https://link.springer.com/content/pdf/10.1007/s00041-022-09951-5.pdf

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