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arXiv · 1405.2153

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

Tuomas Hytönen·Andreas Rosén
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Abstract

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

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Tuomas Hytönen, Andreas Rosén. 2014-05-09. Bounded variation approximation of L_p dyadic martingales and solutions to elliptic equations. https://arxiv.org/abs/1405.2153

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