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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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Littlewood-Paley theory and the T(1) theorem with non doubling measures
TL;DR: In this article, it was shown that the T(1) theorem for n-dimensional Calderon-Zygmund operators, without doubling assumptions, can be proved using the Littlewood-Paley decomposition that is obtained for functions in $L^p(n)$ functions, as in the classical case of homogeneous spaces.
Journal Article
Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability
TL;DR: For disjoint domains in the Euclidean space whose boundaries satisfy a non-degeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries as discussed by the authors.
Book
The Riesz Transform of Codimension Smaller Than One and the Wolff Energy
TL;DR: In this article, the non-negative locally finite Borel measures with bounded Riesz transform were characterized in terms of the Wolff energy, and a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator was given.
Journal ArticleDOI
Characterization of rectifiable measures in terms of -numbers
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Failure of $L^2$ boundedness of gradients of single layer potentials for measures with zero low density
TL;DR: In this paper, it was shown that for a uniformly elliptic operator in divergence form associated with a matrix with Holder continuous coefficients, the Riesz transform is not bounded in O(L 2 ) time.