Sobolev martingales

Rami Ayoush; Dmitriy M. Stolyarov; Michal Wojciechowski

doi:10.4171/rmi/1224

JournalsrmiVol. 37, No. 4pp. 1225–1246

Sobolev martingales

Rami Ayoush
Polish Academy of Sciences, Warsaw, Poland
- MathSciNet
- zbMATH Open
Dmitriy M. Stolyarov
St. Petersburg State University and Steklov Mathematical Institute, St. Petersburg, Russia
- MathSciNet
- zbMATH Open
Michal Wojciechowski
Polish Academy of Sciences, Warsaw, Poland
- MathSciNet
- zbMATH Open

Download PDF

A subscription is required to access this article.

Abstract

We introduce new spaces of martingales that behave like $L_{1}$ -based Sobolev spaces on $R^{d}$ . 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