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
DOI: 10.4171/rmi/1224
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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.