Sobolev martingales

• Rami Ayoush ^[1] ; Dmitriy M. Stolyarov ^[2] ; Michal Wojciechowski ^[1]
  1. [1] Polish Academy of Sciences

     Polish Academy of Sciences

     Warszawa, Polonia

     
  2. [2] St. Petersburg State University
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 4, 2021, págs. 1225-1246
• Idioma: inglés
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• Resumen

  • We introduce new spaces of martingales that behave like L1-based Sobolev spaces on Rd. 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.