Bounded variation approximation of dyadic martingales and solutions to elliptic equations

  • Tuomas Hytönen

    University of Helsinki, Finland
  • Andreas Rosén

    University of Gothenburg, Sweden

Abstract

We prove continuity and surjectivity of the trace map onto , from a space of functions of locally bounded variation, defined by the Carleson functional. The extension map is constructed through a stopping time argument. This extends earlier work by Varopoulos in the BMO case, related to the Corona Theorem. We also prove Carleson approximability results for solutions to elliptic non-smooth divergence form equations, which generalize results in the case by Hofmann, Kenig, Mayboroda and Pipher.

Cite this article

Tuomas Hytönen, Andreas Rosén, Bounded variation approximation of dyadic martingales and solutions to elliptic equations. J. Eur. Math. Soc. 20 (2018), no. 8, pp. 1819–1850

DOI 10.4171/JEMS/800