Abstract
We show that, given a set E ⊂ R n+1 with ffnite n-Hausdorff measure H n , if the n-dimensional Riesz transform RH n bEf(x) =/E/x-y/x-y/ n+1 f(y)H n (y)is bounded in L2(HnbE), then E is n-rectiáble. From this result we deduce that a compact set E ⊂ R n+1 with H n (E) < ∞ is removable for Lipschitz harmonic functions if and only if it is purely n-unrectiáble, thus proving the analog of Vitushkin's conjecture in higher dimensions.
Original language | English |
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Pages (from-to) | 517-532 |
Journal | Publicacions Matematiques |
Volume | 58 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Lipschitz harmonic functions
- Rectifiability
- Riesz transform