Bilipschitz maps, analytic capacity, and the Cauchy integral

• Autores: Xavier Tolsa Domènech
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 3, 2005, págs. 1241-1302
• Idioma: inglés
• DOI: 10.4007/annals.2005.162.1243
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• Resumen

  • Let . : C . C be a bilipschitz map. We prove that if E . C is compact, and .(E), a(E) stand for its analytic and continuous analytic capacity respectively, then C-1.(E) = .(.(E)) = C.(E) and C-1a(E) = a(.(E)) = Ca(E), where C depends only on the bilipschitz constant of .. Further, we show that if µ is a Radon measure on C and the Cauchy transform is bounded on L2(µ), then the Cauchy transform is also bounded on L2(.
    µ), where .
    µ is the image measure of µ by .. To obtain these results, we estimate the curvature of .
    µ by means of a corona type decomposition.