Sobolev martingales
Rami Ayoush
Polish Academy of Sciences, Warsaw, PolandDmitriy M. Stolyarov
St. Petersburg State University and Steklov Mathematical Institute, St. Petersburg, RussiaMichal Wojciechowski
Polish Academy of Sciences, Warsaw, Poland
Abstract
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