Sobolev martingales

  • Rami Ayoush

    Polish Academy of Sciences, Warsaw, Poland
  • Dmitriy M. Stolyarov

    St. Petersburg State University and Steklov Mathematical Institute, St. Petersburg, Russia
  • Michal Wojciechowski

    Polish Academy of Sciences, Warsaw, Poland
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We introduce new spaces of martingales that behave like -based Sobolev spaces on . We prove a martingale analog of Van Schaftingen’s theorem and give sharp estimates on the lower Hausdorff dimension of the terminal distributions of these martingales. We also provide martingale analogs of trace theorems for Sobolev functions.

Cite this article

Rami Ayoush, Dmitriy M. Stolyarov, Michal Wojciechowski, Sobolev martingales. Rev. Mat. Iberoam. 37 (2021), no. 4, pp. 1225–1246

DOI 10.4171/RMI/1224