Bounded variation approximation of $L_p$ dyadic martingales and solutions to elliptic equations

Tuomas Hytönen; Andreas Rosén

doi:10.4171/jems/800

Geodesic

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Bounded variation approximation of

L_{p}

dyadic martingales and solutions to elliptic equations

Tuomas Hytönen ; Andreas Rosén

Journal of the European Mathematical Society, Tome 20 (2018) no. 8, pp. 1819-1850.

Voir la notice de l'article provenant de la source EMS Press

Résumé

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

DOI : 10.4171/jems/800

Classification : 42-XX, 35-XX
Mots-clés : Extension map, Carleson functional, approximability, stopping time argument, Corona Theorem, elliptic equation, bounded variation

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Tuomas Hytönen; Andreas Rosén. Bounded variation approximation of $L_p$ dyadic martingales and solutions to elliptic equations. Journal of the European Mathematical Society, Tome 20 (2018) no. 8, pp. 1819-1850. doi : 10.4171/jems/800. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/800/

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Cité par 8 documents. Sources : zbMATH