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For bilipschitz images of Cantor sets in R d we estimate the Lipschitz harmonic capacity and prove that this capacity is invariant under bilipschitz homeomorphisms. A crucial step of the proof is an estimate of the L 2 norms of the Riesz tranforms on L 2doi:10.4310/mrl.2006.v13.n6.a3 fatcat:peby3dve55e4hfp57bwfdcohzm