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)

Date:	2014
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Riesz transform ; Rectifiability ; Lipschitz harmonic functions
Published in:	Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 517-532, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287189
DOI: 10.5565/PUBLMAT_58214_26

16 p, 405.7 KB

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