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16 p, 405.7 KB The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions / Nazarov, Fedor (Kent State University. Department of Mathematical Sciences) ; Tolsa Domènech, Xavier (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Volberg, Alexander (Michigan State University. Department of Mathematics)
We show that, given a set E Rn+1 with finite n-Hausdorff measure Hn, if the n-dimensional Riesz transform is bounded in L2(HnbE), then E is n-rectifiable. From this result we deduce that a compact set E Rn+1 with Hn(E) < 1 is removable for Lipschitz harmonic functions if and only if it is purely n-unrectifiable, thus proving the analog of Vitushkin's conjecture in higher dimensions.
2014 - 10.5565/PUBLMAT_58214_26
Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 517-532  
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