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).
Bibliographical noteFunding 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: email@example.com (S. Mayboroda), firstname.lastname@example.org, A.Volberg@ed.ac.uk (A. Volberg).