For bilipschitz images of Cantor sets in ℝd 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 L2 norms of the Riesz tranforms on L2(G, p) where p is the natural probability measure on the Cantor set E and G ⊂ E has p(G) > 0. © International Press 2006.
|Journal||Mathematical Research Letters|
|Publication status||Published - 1 Sept 2006|