Images of nowhere differentiable Lipschitz maps of into L_1[0,1]
Tom 243 / 2018
Fundamenta Mathematicae 243 (2018), 75-83
MSC: Primary 46G05; Secondary 46B22.
DOI: 10.4064/fm493-12-2017
Opublikowany online: 24 May 2018
Streszczenie
The main result: for every sequence \{\omega _m\}_{m=1}^\infty of positive numbers 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 infinitely differentiable on [0,1] with \max_{x\in [0,1]}|F_t^{(m)}(x)|\le \omega _m and has an extension to an entire function on the complex plane.
