Bounded variation approximation of Lp Dyadic martingales and solutions to elliptic equations
Journal article, 2018

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.

Extension map

Bounded variation


Carleson functional

Elliptic equation

Corona Theorem

Stopping time argument


Tuomas Hytönen

University of Helsinki

Andreas Rosén

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of the European Mathematical Society

1435-9855 (ISSN) 1435-9863 (eISSN)

Vol. 20 8 1819-1850

Subject Categories

Computational Mathematics


Mathematical Analysis



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