Abstract
The aim of these notes is to provide a new proof of the Mattila-Melnikov-Verdera theorem on the uniform rectifiability of an Ahlfors-David regular measure whose associated Cauchy transform operator is bounded. They are based on lectures given by the second author in the analysis seminars at Kent State University and Tel-Aviv University.
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Notes
- 1.
In the notation of the previous section, \(\Gamma = \Gamma _{\ell_{0}}{\bigl ( \tfrac{\ell(Q)} {2} \bigl )}\), for some \(\ell_{0} \leq \tfrac{\ell(Q)} {2}\).
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Jaye, B., Nazarov, F. (2014). Reflectionless Measures and the Mattila-Melnikov-Verdera Uniform Rectifiability Theorem. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_15
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