DOI

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.

Original languageEnglish
Pages (from-to)1225-1246
Number of pages22
JournalRevista Matematica Iberoamericana
Volume37
Issue number4
DOIs
StatePublished - 2021

    Scopus subject areas

  • Mathematics(all)

    Research areas

  • Hausdorff dimension of measures, Martingale inequalities, Sobolev embedding, Trace theorem, martingale inequalities, INEQUALITIES, SPACES, EQUATIONS, DIV-CURL, VECTOR-FIELDS, trace theorem, H-1

ID: 88986311