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
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Record created 2014-07-10, last modified 2022-10-20