Geodesic
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

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

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
Keywords: Extension map, Carleson functional, approximability, stopping time argument, Corona Theorem, elliptic equation, bounded variation 
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     author = {Tuomas Hyt\"onen and Andreas Ros\'en},
     title = {Bounded variation approximation of $L_p$ dyadic martingales and solutions to elliptic equations},
     journal = {Journal of the European Mathematical Society},
     pages = {1819--1850},
     publisher = {mathdoc},
     volume = {20},
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     year = {2018},
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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

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