Generalized spaces of pointwise regularity: toward a general framework for the WLM

Abstract In this work we generalize the spaces T u p introduced by Calderón and Zygmund using pointwise conditions emanating from generalized Besov spaces. We give conditions binding the functions belonging to these spaces and their wavelet coefficients. Next, we propose a multifractal formalism bas...

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Bibliographic Details
Published inNonlinearity Vol. 34; no. 9; pp. 6561 - 6586
Main Authors Loosveldt, L, Nicolay, S
Format Journal Article Web Resource
LanguageEnglish
Published IOP Publishing 01.09.2021
Institute of Physics Publishing
Subjects
Mathematics
Mathématiques
multifractal formalisms
Physical, chemical, mathematical & earth Sciences
Physique, chimie, mathématiques & sciences de la terre
pointwise regularity spaces
wavelets
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Summary:Abstract In this work we generalize the spaces T u p introduced by Calderón and Zygmund using pointwise conditions emanating from generalized Besov spaces. We give conditions binding the functions belonging to these spaces and their wavelet coefficients. Next, we propose a multifractal formalism based on such spaces which generalizes the so-called wavelet leaders method and show that it is satisfied on a prevalent set.
Bibliography:London Mathematical Society
NON-104508.R1
scopus-id:2-s2.0-85113331585
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ac1724