학술논문
Directional multifractal analysis in the $L^p$ setting.
Document Type
Journal
Author
Ben Slimane, Mourad (SAR-RYADS) AMS Author Profile; Ben Omrane, Ines (SAR-SIUS-DM) AMS Author Profile; Ben Abid, Moez (TN-SOUS-STH) AMS Author Profile; Halouani, Borhen (SAR-RYADS) AMS Author Profile; Alshormani, Farouq (SAR-RYADS) AMS Author Profile
Source
Subject
42 Harmonic analysis on Euclidean spaces -- 42B Harmonic analysis in several variables
42B35Function spaces arising in harmonic analysis
46Functional analysis -- 46E Linear function spaces and their duals
46E30Spaces of measurable functions
42B35
46
46E30
Language
English
ISSN
23148888
Abstract
Summary: ``The classical Hölder regularity is restricted to locallybounded functions and takes only positive values. The local $L^p$regularity covers unbounded functions and negative values.Nevertheless, it has the same apparent regularity in all directions. Inthe present work, we study a recent notion of directional local $L^p$regularity introduced by Jafard. We provide its characterization by asupremum of a wide range oriented anisotropic Triebel waveletcoefficients and leaders. In addition, we deduce estimates on theHausdorf dimension of the set of points where the directional local$L^p$ regularity does not exceed a given value. The obtained resultsare illustrated by some examples of self-affine cascade functions.''