L^2 boundedness of Riesz transforms and rectifiability

Xavier Tolsa
Universitat Autònoma de Barcelona

In the talk I will explain the results of a joint work with Fedor Nazarov and Alexander Volberg where we show that if E is a set in R^{n+1} with finite n-dimensional Hausdorff measure and the n-dimensional Riesz transform with respect to this measure is bounded in L^2, then E is n-rectifiable. In the case of AD-regular measures, this solves the so called David-Semmes problem in codimension 1.

Presentation (PDF File)

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