Abstract
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.
| Original language | English |
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| Pages (from-to) | 865-884 |
| Journal | Mathematical Research Letters |
| Volume | 13 |
| Issue number | 5-6 |
| Publication status | Published - 1 Sept 2006 |