Bounded variation approximation of Lp Dyadic martingales and solutions to elliptic equations
Artikel i vetenskaplig tidskrift, 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

Approximability

Carleson functional

Elliptic equation

Corona Theorem

Stopping time argument

Författare

Tuomas Hytönen

Helsingin Yliopisto

Andreas Rosén

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Journal of the European Mathematical Society

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

Vol. 20 8 1819-1850

Ämneskategorier

Beräkningsmatematik

Geometri

Matematisk analys

DOI

10.4171/JEMS/800

Mer information

Senast uppdaterat

2018-09-19