Directional Multifractal Analysis in the Lp Setting

Directional Multifractal Analysis in the Lp Setting

The classical Hölder regularity is restricted to locally bounded functions and takes only positive values. The local Lp regularity covers unbounded functions and negative values. Nevertheless, it has the same apparent regularity in all directions. In the present work, we study a recent notion of dir...

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Main Authors: Mourad Ben Slimane, Ines Ben Omrane, Moez Ben Abid, Borhen Halouani, Farouq Alshormani
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2019/1691903
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spelling doaj-f6811c427794416ea72df814e12af97e2020-11-25T02:53:05ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/16919031691903Directional Multifractal Analysis in the Lp SettingMourad Ben Slimane0Ines Ben Omrane1Moez Ben Abid2Borhen Halouani3Farouq Alshormani4King Saud University, Department of Mathematics, College of Science, P. O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi ArabiaUniversité de Sousse, Ecole Supérieure des Sciences et de la Technologie de Hammam Sousse, Sousse, TunisiaKing Saud University, Department of Mathematics, College of Science, P. O. Box 2455, Riyadh 11451, Saudi ArabiaKing Saud University, Department of Mathematics, College of Science, P. O. Box 2455, Riyadh 11451, Saudi ArabiaThe classical Hölder regularity is restricted to locally bounded functions and takes only positive values. The local Lp regularity covers unbounded functions and negative values. Nevertheless, it has the same apparent regularity in all directions. In the present work, we study a recent notion of directional local Lp regularity introduced by Jaffard. We provide its characterization by a supremum of a wide range oriented anisotropic Triebel wavelet coefficients and leaders. In addition, we deduce estimates on the Hausdorff dimension of the set of points where the directional local Lp regularity does not exceed a given value. The obtained results are illustrated by some examples of self-affine cascade functions.http://dx.doi.org/10.1155/2019/1691903
collection DOAJ
language English
format Article
sources DOAJ
author Mourad Ben Slimane
Ines Ben Omrane
Moez Ben Abid
Borhen Halouani
Farouq Alshormani
spellingShingle Mourad Ben Slimane
Ines Ben Omrane
Moez Ben Abid
Borhen Halouani
Farouq Alshormani
Directional Multifractal Analysis in the Lp Setting
Journal of Function Spaces
author_facet Mourad Ben Slimane
Ines Ben Omrane
Moez Ben Abid
Borhen Halouani
Farouq Alshormani
author_sort Mourad Ben Slimane
title Directional Multifractal Analysis in the Lp Setting
title_short Directional Multifractal Analysis in the Lp Setting
title_full Directional Multifractal Analysis in the Lp Setting
title_fullStr Directional Multifractal Analysis in the Lp Setting
title_full_unstemmed Directional Multifractal Analysis in the Lp Setting
title_sort directional multifractal analysis in the lp setting
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2019-01-01
description The classical Hölder regularity is restricted to locally bounded functions and takes only positive values. The local Lp regularity covers unbounded functions and negative values. Nevertheless, it has the same apparent regularity in all directions. In the present work, we study a recent notion of directional local Lp regularity introduced by Jaffard. We provide its characterization by a supremum of a wide range oriented anisotropic Triebel wavelet coefficients and leaders. In addition, we deduce estimates on the Hausdorff dimension of the set of points where the directional local Lp regularity does not exceed a given value. The obtained results are illustrated by some examples of self-affine cascade functions.
url http://dx.doi.org/10.1155/2019/1691903
work_keys_str_mv AT mouradbenslimane directionalmultifractalanalysisinthelpsetting
AT inesbenomrane directionalmultifractalanalysisinthelpsetting
AT moezbenabid directionalmultifractalanalysisinthelpsetting
AT borhenhalouani directionalmultifractalanalysisinthelpsetting
AT farouqalshormani directionalmultifractalanalysisinthelpsetting
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