Lipschitz harmonic capacity and bilipschitz images of Cantor sets

John Garnett, Laura Prat, Xavier Tolsa

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

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 languageEnglish
Pages (from-to)865-884
JournalMathematical Research Letters
Volume13
Issue number5-6
Publication statusPublished - 1 Sep 2006

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