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

Volume 243 / 2018

Florin Catrina, Mikhail I. Ostrovskii Fundamenta Mathematicae 243 (2018), 75-83 MSC: Primary 46G05; Secondary 46B22. DOI: 10.4064/fm493-12-2017 Published online: 24 May 2018

Abstract

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.

Authors

  • Florin CatrinaDepartment of Mathematics and Computer Science
    St. John’s University
    8000 Utopia Parkway
    Queens, NY 11439, U.S.A.
    e-mail
  • Mikhail I. OstrovskiiDepartment of Mathematics and Computer Science
    St. John’s University
    8000 Utopia Parkway
    Queens, NY 11439, U.S.A.
    e-mail

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