© 2015, Springer-Verlag Berlin Heidelberg. We consider the Calderón–Zygmund kernels (Formula presentd.) in Rd for 0<α≤1 and n∈N. We show that, on the plane, for 0<α<1, the capacity associated to the kernels Kα,n is comparable to the Riesz capacity (Formula presented.) of non-linear potential theory. As consequences we deduce the semiadditivity and bilipschitz invariance of this capacity. Furthermore we show that for any Borel set E⊂Rd with finite length the L2(H1⌊E)-boundedness of the singular integral associated to K1,n implies the rectifiability of the set E. We thus extend to any ambient dimension, results previously known only in the plane.