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Xavier Tolsa

  1. Harmonic measure and quantitative connectivity: geometric characterization of the Lp-solvability of the Dirichlet problem
    2020/07/20 by Jonas Azzam, Steve Hofmann, José María Martell +2 · 9 citations
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research
  2. Harmonic measure and quantitative connectivity: geometric characterization of the Lp solvability of the Dirichlet problem. Part II
    2018/03/21 by Jonas Azzam, Mihalis Mourgoglou, Azzam, Jonas +3 · 5 citations
    Computer Science · Mathematics · #28A75 #28A78 #31B15 #35J08 #35J15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
  3. Painleve's problem and the semiadditivity of analytic capacity
    2002/04/02 by Xavier Tolsa, Tolsa, Xavier · 4 citations
    Mathematics · #30C85 #42B20 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.CA #msc:30C85 #msc:42B20
  4. The regularity problem for the Laplace equation in rough domains
    2021/10/05 by Mihalis Mourgoglou, Mourgoglou, Mihalis, Xavier Tolsa +1 · 5 citations
    Computer Science · Mathematics · #28A78 #31B05 #31B20 #35J05 #35J25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
  5. A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decomposition
    2000/02/25 by Xavier Tolsa, Tolsa, Xavier · 2 citations
    Mathematics · #42B20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.CA #math.FA #msc:42B20
  6. Littlewood-Paley theory and the T(1) theorem with non doubling measures
    2000/06/05 by Xavier Tolsa, Tolsa, Xavier · 2 citations
    Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #advanced mathematical theories #math.CA #math.FA #msc:42B20 #msc:42B30
  7. Solvability of the Poisson-Dirichlet problem with interior data in Lp'-Carleson spaces and its applications to the Lp-regularity problem
    2022/07/21 by Mihalis Mourgoglou, Bruno Poggi, Mourgoglou, Mihalis +3 · 4 citations
    Mathematics · #31B20 #31B35 #35B30 #35J05 #35J15 #35J25 (Primary) 35J08 #42B25 #42B35 #42B37 (Secondary) #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations
  8. On the uniform rectifiability of AD regular measures with bounded Riesz transform operator: the case of codimension 1
    2012/12/20 by Fedor Nazarov, Fëdor Nazarov, Nazarov, Fedor +4 · 5 citations
    Mathematics · #35R35 #42B20 #49Q15 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations #acm:35R35 #acm:42B20 #acm:49Q15 #advanced mathematical theories #math.AP #math.CA #msc:35R35 #msc:42B20 #msc:49Q15
  9. The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions
    2012/12/21 by Fedor Nazarov, Fëdor Nazarov, Xavier Tolsa +4 · 2 citations
    Computer Science · Mathematics · #28A75 #42B20 #47B40 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #math.AP #math.CA #msc:28A75 #msc:42B20 #msc:47B40
  10. Analytic capacity and projections
    2017/12/02 by Alan Chang, Chang, Alan, Xavier Tolsa +1 · 2 citations
    Mathematics · #Mathematical Approximation and Integration #Advanced Harmonic Analysis Research #Analytic and geometric function theory
  11. The Riesz transform and quantitative rectifiability for general Radon\n measures
    2016/01/29 by Daniel Girela-Sarrión, Xavier Tolsa, Girela-Sarrión, Daniel +1 · 1 citation
    Computer Science · Mathematics · #28A75 #28A78 #42B20 #49Q20 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations
  12. Mutual absolute continuity of interior and exterior harmonic measure\n implies rectifiability
    2016/02/03 by Jonas Azzam, Azzam, Jonas, Mihalis Mourgoglou +3 · 2 citations
    Computer Science · Mathematics · #28A75 #28A78 #31A15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG) #Numerical methods in inverse problems
  13. The Riesz transform of codimension smaller than one and the Wolff energy
    2016/02/08 by Benjamin Jaye, Fedor Nazarov, Jaye, Benjamin +5 · 1 citation
    Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AP #math.CA
  14. Failure of L2 boundedness of gradients of single layer potentials for measures with zero low density
    2018/01/25 by José M. Conde‐Alonso, Mihalis Mourgoglou, Conde-Alonso, José M. +3 · 1 citation
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
  15. L2-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type
    2021/12/14 by Alejandro Molero, Molero, Alejandro, Mihalis Mourgoglou +5 · 1 citation
    Computer Science · Mathematics · #28A75 #33C55 #35J15 #42B20 #42B37 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
  16. The dimension of harmonic measure on some AD-regular flat sets of fractional dimension
    2023/01/10 by Xavier Tolsa, Tolsa, Xavier · 1 citation
    Computer Science · Mathematics · #31B15 #31B20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations
  17. Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains
    2024/07/29 by Mihalis Mourgoglou, Mourgoglou, Mihalis, Xavier Tolsa +1 · 2 citations
    Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Nonlinear Partial Differential Equations
  18. The measures with L2-bounded Riesz transform and the Painlevé problem
    2024/01/12 by Damian Dąbrowski, Xavier Tolsa, Dąbrowski, Damian +1 · 1 citation
    Computer Science · Mathematics · #28A75 #42B20 #49Q15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems