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. 1819–1850DOI 10.4171/JEMS/800