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Xavier Tolsa
Researcher at Autonomous University of Barcelona
Publications - 169
Citations - 3994
Xavier Tolsa is an academic researcher from Autonomous University of Barcelona. The author has contributed to research in topics: Bounded function & Measure (mathematics). The author has an hindex of 30, co-authored 160 publications receiving 3658 citations. Previous affiliations of Xavier Tolsa include Chalmers University of Technology & Catalan Institution for Research and Advanced Studies.
Papers
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Journal ArticleDOI
Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient
Albert Clop,Xavier Tolsa +1 more
TL;DR: In this paper, it was shown that a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space preserves sets with vanishing analytic capacity.
Posted Content
The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions
TL;DR: In this paper, it was shown that a compact Lipschitz harmonic function can be removed if and only if it is purely $n$-unrectifiable, thus proving the analog of Vitushkin's conjecture in higher dimensions.
Book ChapterDOI
Estimate of the Cauchy Integral over Ahlfors Regular Curves
Mark Melnikov,Xavier Tolsa +1 more
TL;DR: In this article, the authors obtained the complete characterization of domains G ⊂ ℂ which admit the so-called estimate of the Cauchy integral, that is to say, for all E ∊ G and f ∊ H ∞ (G E), where γ is the analytic capacity of E. The corresponding result for continuous functions f and the continuous analytic capacity α(E) is also proved.
Journal ArticleDOI
Analytic capacity and projections
Alan Chang,Xavier Tolsa +1 more
TL;DR: The connection between the analytic capacity of a set and the size of its orthogonal projections was studied in this article, where it was shown that if the set is compact and the Borel measure supported on the set supports the projection, then the analytical capacity of the set satisfies the following property.
Journal ArticleDOI
Quasiconformal distortion of riesz capacities and hausdorff measures in the plane
TL;DR: In this article, the sharp distortion estimates for the quasi-conformal mappings in the plane were proved in terms of the Riesz capacities from non-linear potential theory and the Hausdorff measures.