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Bounded variation approximation of Lp Dyadic martingales and solutions to elliptic equations

Journal article
Authors Tuomas Hytönen
Andreas Rosén
Published in Journal of the European Mathematical Society
Volume 20
Issue 8
Pages 1819-1850
ISSN 1435-9855
Publication year 2018
Published at Department of Mathematical Sciences
Pages 1819-1850
Language en
Keywords Approximability, Bounded variation, Carleson functional, Corona Theorem, Elliptic equation, Extension map, Stopping time argument
Subject categories Mathematical Analysis, Geometry, Computational Mathematics


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 LpCarleson approximability results for solutions to elliptic non-smooth divergence form equations, which generalize results in the case p = ∞ by Hofmann, Kenig, Mayboroda and Pipher.

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