Calderon-Zygmund capacities and Wolff potentials on Cantor sets

We show that, for some Cantor sets in R^d, the capacity g_s associated to the s-dimensional Riesz kernel x/|x|^{s+1} is comparable to the capacity C_{2(d-s)/3,3/2} from non linear potential theory. It is an open problem to show that, when s is positive and non integer, they are comparable for all compact sets in R^d. We also discuss other open questions in the area.

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