Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in $T_p^\alpha (x)$

Loosveldt, Laurent; Nicolay, Samuel

doi:10.1007/s00041-022-09951-5

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Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in $T_p^\alpha (x)$

Loosveldt, Laurent; Nicolay, Samuel

2022 • In Journal of Fourier Analysis and Applications, 28 (4)

Peer reviewed

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https://hdl.handle.net/2268/292865

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10.1007/s00041-022-09951-5

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Keywords :

Applied Mathematics; General Mathematics; Analysis

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 $x_0$ .

Disciplines :

Mathematics

Author, co-author :

Loosveldt, Laurent ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Nicolay, Samuel ; Université de Liège - ULiège > Mathematics

Language :

English

Title :

Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in $T_p^\alpha (x)$

Publication date :

01 July 2022

Journal title :

Journal of Fourier Analysis and Applications

ISSN :

1069-5869

eISSN :

1531-5851

Publisher :

Springer Science and Business Media LLC

Volume :

Issue :

Peer reviewed :

Peer reviewed

Additional URL :

https://link.springer.com/content/pdf/10.1007/s00041-022-09951-5.pdf

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since 02 July 2022

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