Journal d'Analyse Mathématique

, Volume 137, Issue 1, pp 73–100 | Cite as

Regularity and modulus of continuity of space-filling curves

  • Aapo Kauranen
  • Pekka Koskela
  • Aleksandra ZapadinskayaEmail author


We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example.


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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • Aapo Kauranen
    • 1
  • Pekka Koskela
    • 2
  • Aleksandra Zapadinskaya
    • 3
    Email author
  1. 1.Department of MathematicsAutonomous University of BarcelonaBellaterra (Barcelona)Spain
  2. 2.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland
  3. 3.Department of MathematicsUniversity of PisaPisaItaly

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