Calderon-Zygmund capacities and Wolff potentials on Cantor sets
Classical Analysis and ODEs
2013-02-01 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1001.2986,
title = {Calderon-Zygmund capacities and Wolff potentials on Cantor sets},
author = {Xavier Tolsa},
journal= {arXiv preprint arXiv:1001.2986},
year = {2013}
}
Comments
Minor corrections in Lemma 5.11