Variation for Riesz transforms and uniform rectifiability
Albert Mas,
(UPV/EHU)
Viernes 20 de enero 2012
I will present the following result, which is a joint work with Xavier Tolsa: {let 0 < n < d be integers and let \mu be an n-dimensional AD regular measure in \R^d. Then, \mu is uniformly n-rectifiable if and only if the variation for the Riesz transforms with respect to \mu is a bounded operator in L^2(\mu)}. This result is related to an important open problem, posed by David and Semmes, about the equivalence between uniform rectifiability and L^2 boundedness of the Riesz transforms. I will give the basic definitions, the motivation, and some ideas of the proof.