Pointwise smoothness of space-filling functions

Stéphane Jaffard (1) , Samuel Nicolay (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Département de Mathématiques [Liège]

We study irregularity properties of generic Peano functions; we apply these results to the determination of the pointwise smoothness of a Peano function introduced by Lebesgue and of some related functions, showing that they are either monoh ̈older or multifractal functions. We test on these examples several numerical variants of the multifractal formalism, and we show how a change of topology on IR can affect the H ̈older regularity of such functions.

Domaines: Analyse classique [math.CA]

Stéphane Jaffard, Samuel Nicolay. Pointwise smoothness of space-filling functions. Applied and Computational Harmonic Analysis, 2009, 26 (2), pp.181-199. ⟨hal-00798379⟩