Mathematical Research Letters

Volume 13, Issue 6, November 2006 pp. 865-884.

Lipschitz harmonic capacity and Bilipschitz images of cantor sets

Authors: John Garnett (1), Laura Prat (2), Xavier Tolsa (3)
Author institution: UCLA (1), Universitat de Barcelona (2), Universitat Autónoma de Barcelona

Summary: 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 $L^2$ norms of the Riesz tranforms on $L^2(G,p)$ where $p$ is the natural probability measure on the Cantor set $E$ and $G \subset E$ has $p(G) > 0.$

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