Pointwise smoothness of space-filling functions (Q1006628)

The authors study irregularity properties of generic Peano functions. They apply these results to the determination of the pointwise smoothness of a Peano function introduced by Lebesgue and of some related functions, showing that these functions are either monohölder or multifractal functions. They test on these examples several numerical variants of the multifractal formalism, and they show how a change of topology on \(R\) can affect the Hölder regularity of such functions.