65 citations · 398 across the 74 of their papers we have counts for
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Capacities associated with Calderón-Zygmund kernels
Vasilis Chousionis, Joan Mateu, Laura Prat +1
Analytic capacity is associated with the Cauchy kernel and the -norm. For , one has likewise capacities related to the kernels $K_i(x)=x_i^{2n-1}/|x…
Calderón-Zygmund kernels and rectifiability in the plane
Vasilis Chousionis, Joan Mateu, Laura Prat +1
Let $E \subset \C$ be a Borel set with finite length, that is, . By a theorem of David and Léger, the -boundedness of the…
Variation for the Riesz transform and uniform rectifiability
Albert Mas, Xavier Tolsa
For 0<n<d integers and r>2, we prove that an n-dimensional Ahlfors-David regular measure M in R^d is uniformly n-rectifiable if and only if the r-variation for the Riesz transform…
Mass transport and uniform rectifiability
Xavier Tolsa
In this paper we characterize the so called uniformly rectifiable sets of David and Semmes in terms of the Wasserstein distance from optimal mass transport. To obtain this re…
Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs
Albert Mas, Xavier Tolsa
We prove that, for r>2, the r-variation and oscillation for the smooth truncations of the Cauchy transform on Lipschitz graphs are bounded in L^p for 1<p finite. The analogous resu…