Boundedness of the square function and rectifiability

Svitlana Mayboroda, Alexander Volberg

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Following a recent paper [X. Tolsa, Principal values for Riesz transforms and rectifiability, J. Funct. Anal. 254 (7) (2008) 1811-1863] we show that the finiteness of the square function associated with the Riesz transforms with respect to Hausdorff measure Hn (n is an integer) on a set E, implies that E is rectifiable. To cite this article: S. Mayboroda, A. Volberg, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

Original languageEnglish (US)
Pages (from-to)1051-1056
Number of pages6
JournalComptes Rendus Mathematique
Volume347
Issue number17-18
DOIs
StatePublished - Sep 2009

Bibliographical note

Funding Information:
✩ The first author was partially supported by the NSF grant 0929382. The second author was partially supported by the NSF grant 0758552. E-mail addresses: svitlana@math.purdue.edu (S. Mayboroda), volberg@math.msu.edu, A.Volberg@ed.ac.uk (A. Volberg).

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