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Xavier Tolsa

Identifiers

  • name variant Xavier Tolsa 0.60 · backfill

Papers (61)

  1. Dimension Drop for Harmonic Measure on Ahlfors Regular Boundaries math.AP · 2026 · author #2
  2. The mutual singularity of harmonic measure and Hausdorff measure of codimension smaller than one math.CA · 2019 · author #1
  3. On $C^1$-approximability of functions by solutions of second order elliptic equations on plane compact sets and $C$-analytic capacity math.CA · 2018 · author #2
  4. Characterization of rectifiable measures in terms of $\alpha$-numbers math.CA · 2018 · author #2
  5. Harmonic measure and quantitative connectivity: geometric characterization of the $L^p$ solvability of the Dirichlet problem. Part II math.AP · 2018 · author #3
  6. A family of singular integral operators which control the Cauchy transform math.CA · 2018 · author #3
  7. Failure of $L^2$ boundedness of gradients of single layer potentials for measures with zero low density math.CA · 2018 · author #3
  8. Analytic capacity and projections math.CA · 2017 · author #2
  9. Rectifiability of measures and the $\beta_p$ coefficients math.CA · 2017 · author #1
  10. The measures with an associated square function operator bounded in $L^2$ math.CA · 2016 · author #3
  11. Uniform rectifiability, elliptic measure, square functions, and $\varepsilon$-approximability via an ACF monotonicity formula math.CA · 2016 · author #4
  12. Uniform rectifiability from Carleson measure estimates and $\varepsilon$-approximability of bounded harmonic functions math.CA · 2016 · author #3
  13. On a two-phase problem for harmonic measure in general domains math.CA · 2016 · author #3
  14. On Tsirelson's theorem about triple points for harmonic measure math.CA · 2016 · author #1
  15. Singular integrals unsuitable for the curvature method whose $L^2$-boundedness still implies rectifiability math.CA · 2016 · author #3
  16. The one-phase problem for harmonic measure in two-sided NTA domains math.CA · 2016 · author #3
  17. The Riesz transform of codimension smaller than one and the Wolff energy math.AP · 2016 · author #4
  18. Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability math.CA · 2016 · author #3
  19. The Riesz transform and quantitative rectifiability for general Radon measures math.CA · 2016 · author #2
  20. Improved Cotlar's inequality in the context of local $Tb$ theorems math.CA · 2015 · author #3
  21. Harmonic measure and Riesz transform in uniform and general domains math.CA · 2015 · author #2
  22. Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure math.CA · 2015 · author #6
  23. Rectifiability of harmonic measure math.CA · 2015 · author #6
  24. Absolute continuity between the surface measure and harmonic measure implies rectifiability math.AP · 2015 · author #4
  25. Rectifiability of harmonic measure in domains with porous boundaries math.CA · 2015 · author #3
  26. Lp-estimates for the variation for singular integrals on uniformly rectifiable sets math.CA · 2015 · author #2
  27. Non-existence of reflectionless measures for the s-Riesz transform when 0<s<1 math.FA · 2015 · author #2
  28. Singular sets for harmonic measure on locally flat domains with locally finite surface measure math.CA · 2015 · author #3
  29. Characterization of $n$-rectifiability in terms of Jones' square function: Part II math.CA · 2015 · author #2
  30. Characterization of $n$-rectifiability in terms of Jones' square function: Part I math.CA · 2015 · author #1
  31. Square functions of fractional homogeneity and Wolff potentials math.CA · 2014 · author #3
  32. Rectifiable measures, square functions involving densities, and the Cauchy transform math.CA · 2014 · author #1
  33. A T(P) theorem for Sobolev spaces on domains math.CA · 2014 · author #2
  34. Riesz transforms of non-integer homogeneity on uniformly disconnected sets math.CA · 2014 · author #2
  35. Rectifiability via a square function and Preiss' theorem math.CA · 2014 · author #1
  36. Square functions and uniform rectifiability math.CA · 2014 · author #4
  37. Uniform measures and uniform rectifiability math.CA · 2013 · author #1
  38. Strong and weak type estimates for singular integrals with respect to measures separated by AD-regular boundaries math.CA · 2013 · author #2
  39. The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions math.CA · 2012 · author #2
  40. On the uniform rectifiability of AD regular measures with bounded Riesz transform operator: the case of codimension 1 math.AP · 2012 · author #2
  41. Regularity of C^1 and Lipschitz domains in terms of the Beurling transform math.CA · 2012 · author #1
  42. Smoothness of the Beurling transform in Lipschitz domains math.CA · 2012 · author #2
  43. Capacities associated with Calder\'on-Zygmund kernels math.CA · 2011 · author #4
  44. Calder\'on-Zygmund kernels and rectifiability in the plane math.CA · 2011 · author #4
  45. Variation for the Riesz transform and uniform rectifiability math.CA · 2011 · author #2
  46. Mass transport and uniform rectifiability math.CA · 2011 · author #1
  47. Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs math.CA · 2011 · author #2
  48. Calderon-Zygmund capacities and Wolff potentials on Cantor sets math.CA · 2010 · author #1
  49. Hausdorff measure of quasicircles math.CV · 2009 · author #2
  50. Quasiconformal distortion of Hausdorff measures math.CA · 2009 · author #1
  51. Non existence of principal values of signed Riesz transforms of non integer dimension math.CA · 2008 · author #2
  52. Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality math.CA · 2008 · author #1
  53. Principal values for Riesz transforms and rectifiability math.CA · 2007 · author #1
  54. On the smoothness of H\"older-doubling measures math.CA · 2007 · author #2
  55. Bilipschitz maps, analytic capacity, and the Cauchy integral math.CA · 2003 · author #1
  56. Painleve's problem and the semiadditivity of analytic capacity math.CA · 2002 · author #1
  57. Weighted norm inequalities for Calderon-Zygmund operators without doubling conditions math.CA · 2001 · author #1
  58. Littlewood-Paley theory and the T(1) theorem with non doubling measures math.CA · 2000 · author #1
  59. Characterization of the atomic space $H^1$ for non doubling measures in terms of a grand maximal operator math.CA · 2000 · author #1
  60. A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decomposition math.CA · 2000 · author #1
  61. BMO, H^1, and Calderon-Zygmund operators for non doubling measures math.CA · 2000 · author #1

Mentions

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Frequent Coauthors