Bilipschitz maps, analytic capacity, and the Cauchy integral
| dc.creator | Tolsa, Xavier | |
| dc.date | 2003-03-19 | |
| dc.date | 2007-05-23 | |
| dc.date.accessioned | 2026-07-07T08:06:06Z | |
| dc.date.available | 2026-07-07T08:06:06Z | |
| dc.description | Let vphi:C rightarrow C be a bilipschitz map. We prove that if E\subset\C is compact, and gamma(E), alpha(E) stand for its analytic and continuous analytic capacity respectively, then C^{-1}γ(E)\leq γ(\vphi(E)) \leq Cγ(E) and C^{-1}α(E)\leq α(\vphi(E)) \leq Cα(E), where C depends only on the bilipschitz constant of vphi. Further, we show that if mu is a Radon measure on C and the Cauchy transform is bounded on L^2(μ), then the Cauchy transform is also bounded on L^2(\vphi_\sharpμ), where vphi_\sharpμis the image measure of mu by vphi. To obtain these results, we estimate the curvature of vphi_\sharpμby means of a corona type decomposition. | |
| dc.description | 62 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0303243 | |
| dc.identifier | http://arxiv.org/abs/math/0303243 | |
| dc.identifier | Ann. of Math. (2) 162 (2005), no. 3, 1243--1304 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130491 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B20,30E20 | |
| dc.title | Bilipschitz maps, analytic capacity, and the Cauchy integral | |
| dc.type | text |