Images of nowhere differentiable Lipschitz maps of $[0,1]$ into $L_1[0,1]$

Florin Catrina, Mikhail I. Ostrovskii

Published 2017-05-24Version 1

The main result: for every $m\in\mathbb{N}$ and $\omega>0$ there exists an isometric embedding $F:[0,1]\to L_1[0,1]$ which is nowhere differentiable, but for each $t\in [0,1]$ the image $F_t$ is an $m$-times continuously differentiable function with absolute values of all of its $m$ derivatives bounded from above by $\omega$.