On the Baire Generic Validity of the t-Multifractal Formalism in Besov and Sobolev Spaces
Joint Authors
Ben Slimane, Mourad
Ben Omrane, Ines
Ben Abid, Moez
Halouani, Borhen
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-29
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
The t-multifractal formalism is a formula introduced by Jaffard and Mélot in order to deduce the t-spectrum of a function f from the knowledge of the (p,t)-oscillation exponent of f.
The t-spectrum is the Hausdorff dimension of the set of points where f has a given value of pointwise Lt regularity.
The (p,t)-oscillation exponent is measured by determining to which oscillation spaces Op,ts (defined in terms of wavelet coefficients) f belongs.
In this paper, we first prove embeddings between oscillation and Besov-Sobolev spaces.
We deduce a general lower bound for the (p,t)-oscillation exponent.
We then show that this lower bound is actually equality generically, in the sense of Baire’s categories, in a given Sobolev or Besov space.
We finally investigate the Baire generic validity of the t-multifractal formalism.
American Psychological Association (APA)
Ben Abid, Moez& Ben Slimane, Mourad& Ben Omrane, Ines& Halouani, Borhen. 2019. On the Baire Generic Validity of the t-Multifractal Formalism in Besov and Sobolev Spaces. Journal of Function Spaces،Vol. 2019, no. 2019, pp.1-14.
https://search.emarefa.net/detail/BIM-1174756
Modern Language Association (MLA)
Ben Abid, Moez…[et al.]. On the Baire Generic Validity of the t-Multifractal Formalism in Besov and Sobolev Spaces. Journal of Function Spaces No. 2019 (2019), pp.1-14.
https://search.emarefa.net/detail/BIM-1174756
American Medical Association (AMA)
Ben Abid, Moez& Ben Slimane, Mourad& Ben Omrane, Ines& Halouani, Borhen. On the Baire Generic Validity of the t-Multifractal Formalism in Besov and Sobolev Spaces. Journal of Function Spaces. 2019. Vol. 2019, no. 2019, pp.1-14.
https://search.emarefa.net/detail/BIM-1174756
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174756