JournalsjemsVol. 20, No. 8pp. 1819–1850

Bounded variation approximation of LpL_p dyadic martingales and solutions to elliptic equations

  • Tuomas Hytönen

    University of Helsinki, Finland
  • Andreas Rosén

    University of Gothenburg, Sweden
Bounded variation approximation of $L_p$ dyadic martingales and solutions to elliptic equations cover

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Abstract

We prove continuity and surjectivity of the trace map onto Lp(Rn)L_p(\mathbb R^n), 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 LpL_p Carleson approximability results for solutions to elliptic non-smooth divergence form equations, which generalize results in the case p=p=\infty by Hofmann, Kenig, Mayboroda and Pipher.

Cite this article

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

DOI 10.4171/JEMS/800