Xavier Tolsa
#62,916
Most Influential Person Now
Catalan mathematician
Xavier Tolsa's AcademicInfluence.com Rankings
Xavier Tolsamathematics Degrees
Mathematics
#2967
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#4469
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Harmonic Analysis
#15
World Rank
#16
Historical Rank
Measure Theory
#1001
World Rank
#1295
Historical Rank
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Mathematics
Why Is Xavier Tolsa Influential?
(Suggest an Edit or Addition)According to Wikipedia, Xavier Tolsa is a Catalan mathematician, specializing in analysis. Tolsa is a professor at the Autonomous University of Barcelona and at the Institució Catalana de Recerca i Estudis Avançats , the Catalan Institute for Advanced Scientific Studies.
Xavier Tolsa's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Painlevé's problem and the semiadditivity of analytic capacity (2002) (308)
- $BMO, H^1$, and Calderón-Zygmund operators for non doubling measures (2000) (203)
- Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory (2013) (181)
- On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1 (2012) (145)
- Littlewood–Paley Theory and the T(1) Theorem with Non-doubling Measures (2000) (129)
- $L^2$-boundedness of the Cauchy integral operator for continuous measures (1999) (126)
- On the analytic capacity γ (2002) (124)
- The space ¹ for nondoubling measures in terms of a grand maximal operator (2002) (108)
- Characterization of n-rectifiability in terms of Jones’ square function: Part II (2015) (99)
- Uniform rectifiability, Calderón–Zygmund operators with odd kernel, and quasiorthogonality (2008) (84)
- A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition (2000) (84)
- COTLAR'S INEQUALITY WITHOUT THE DOUBLING CONDITION AND EXISTENCE OF PRINCIPAL VALUES FOR THE CAUCHY INTEGRAL OF MEASURES (1998) (73)
- Rectifiability of harmonic measure (2015) (71)
- The capacity γ (2014) (67)
- Characterization of n-rectifiability in terms of Jones’ square function: part I (2015) (64)
- The semiadditivity of continuous analytic capacity and the inner boundary conjecture (2004) (62)
- Principal values for Riesz transforms and rectifiability (2007) (53)
- The planar Cantor sets of zero analytic capacity and the local T(b)-theorem (2002) (48)
- The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions (2012) (47)
- Rectifiable measures, square functions involving densities, and the Cauchy transform (2014) (40)
- Principal values for the Cauchy integral and rectifiability (2000) (39)
- Analytic capacity, rectifiability, and the Cauchy integral (2006) (38)
- Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions (2016) (37)
- Variation for the Riesz transform and uniform rectifiability (2011) (34)
- Riesz Transforms and Harmonic Lip1‐Capacity in Cantor Sets (2004) (32)
- Bilipschitz maps, analytic capacity, and the Cauchy integral (2003) (31)
- A T(1) Theorem for Non‐Doubling Measures with Atoms (2001) (30)
- Rectifiability via a square function and Preiss' theorem (2014) (28)
- Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability (2016) (28)
- A T(P) theorem for Sobolev spaces on domains (2014) (27)
- Calderón–Zygmund kernels and rectifiability in the plane☆ (2011) (27)
- Harmonic measure and Riesz transform in uniform and general domains (2015) (27)
- On the smoothness of Hölder doubling measures (2009) (25)
- Uniform measures and uniform rectifiability (2013) (25)
- Singular sets for harmonic measure on locally flat domains with locally finite surface measure (2015) (25)
- Uniform Rectifiability, Elliptic Measure, Square Functions, and ε-Approximability Via an ACF Monotonicity Formula (2021) (24)
- Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs (2011) (22)
- Mass Transport and Uniform Rectifiability (2011) (22)
- L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels (2004) (19)
- Non existence of principal values of signed Riesz transforms of non integer dimension (2008) (19)
- Calderón-Zygmund Capacities and Wolff Potentials on Cantor Sets (2010) (18)
- On a two-phase problem for harmonic measure in general domains (2016) (17)
- Square functions and uniform rectifiability (2014) (17)
- And Calder´on -zygmund Operators for Non Doubling Measures (2000) (15)
- Smoothness of the Beurling transform in Lipschitz domains (2012) (15)
- Characterization of rectifiable measures in terms of 𝛼-numbers (2018) (15)
- The Riesz transform and quantitative rectifiability for general Radon measures (2016) (15)
- Painlevé's problem and analytic capacity (2006) (14)
- Regularity of C1 and Lipschitz domains in terms of the Beurling transform (2012) (14)
- Harmonic measure and quantitative connectivity: geometric characterization of the $L^p$ solvability of the Dirichlet problem. Part II (2018) (13)
- Uniform rectifiability, elliptic measure, square functions, and $\varepsilon$-approximability (2016) (13)
- Rectifiability of measures and the $\beta_p$ coefficients (2017) (12)
- On the smoothness of H\"older-doubling measures (2007) (12)
- Growth Estimates for Cauchy Integrals of Measures and Rectifiability (2007) (11)
- May the Cauchy transform of a non-trivial finite measure vanish on the support of the measure? (2006) (11)
- Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant (2020) (11)
- Capacities Associated with Calderón-Zygmund Kernels (2013) (10)
- A two-phase free boundary problem for harmonic measure and uniform rectifiability (2017) (10)
- The Riesz Transform of Codimension Smaller Than One and the Wolff Energy (2016) (9)
- Rectifiability of harmonic measure in domains with porous boundaries (2015) (9)
- Estimate of the Cauchy Integral over Ahlfors Regular Curves (2005) (9)
- Characterization and semiadditivity of the ¹-harmonic capacity (2010) (9)
- Absolute continuity between the surface measure and harmonic measure implies rectifiability (2015) (9)
- Jump formulas for singular integrals and layer potentials on rectifiable sets (2018) (9)
- Riesz transforms of non-integer homogeneity on uniformly disconnected sets (2014) (8)
- The regularity problem for the Laplace equation in rough domains (2021) (8)
- Analytic capacity and projections (2017) (8)
- L2-boundedness of gradients of single-layer potentials and uniform rectifiability (2018) (8)
- Lipschitz harmonic capacity and Bilipschitz images of cantor sets (2006) (7)
- $L^2$ boundedness of the Cauchy transform implies $L^2$ boundedness of all antisymmetric Calderón-Zygmund operators associated to odd kernels (2004) (7)
- Finite curvature of arc length measure implies rectifiability: a new proof (2005) (7)
- Improved Cotlar's inequality in the context of local $Tb$ theorems (2015) (7)
- Failure of $$L^2$$L2 boundedness of gradients of single layer potentials for measures with zero low density (2018) (7)
- Characterization of the atomic space $H^1$ for non-doubling measures in terms of a grand maximal operator (2000) (6)
- Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane (2010) (6)
- Weighted norm inequalities for Calderón-Zygmund operators without doubling conditions (2001) (6)
- The measures with $L^2$-bounded Riesz transform satisfying a subcritical Wolff-type energy condition (2021) (6)
- On the semiadditivity of analytic capacity and planar Cantor sets (2003) (6)
- Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient (2008) (6)
- Lp-estimates for the variation for singular integrals on uniformly rectifiable sets (2015) (6)
- Singular integrals unsuitable for the curvature method whose L2-boundedness still implies rectifiability (2016) (5)
- A family of singular integral operators which control the Cauchy transform (2018) (5)
- A proof of Carleson's 𝜀2-conjecture (2019) (5)
- On Tsirelson's theorem about triple points for harmonic measure (2016) (5)
- The measures with $L^2$-bounded Riesz transform and the Painlev\'e problem for Lipschitz harmonic functions (2021) (5)
- The two-phase problem for harmonic measure in VMO (2019) (5)
- Hausdorff measure of quasicircles (2009) (5)
- The measures with an associated square function operator bounded in L2 (2016) (5)
- Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure (2015) (4)
- A geometric characterization of the weak-$A_\infty$ condition for harmonic measure (2018) (4)
- The one-phase problem for harmonic measure in two-sided NTA domains (2016) (3)
- Square functions of fractional homogeneity and Wolff potentials (2014) (2)
- The Mutual Singularity of Harmonic Measure and Hausdorff Measure of Codimension Smaller than One (2019) (2)
- Removable singularities for Lipschitz caloric functions in time varying domains (2020) (2)
- E'S PROBLEM, ANALYTIC CAPACITY AND CURVATURE OF MEASURES (2005) (2)
- QUASICONFORMAL DISTORTION OF HAUSDORFF MEASURES (2009) (2)
- Quasiconformal maps, analytic capacity, and non linear potentials (2009) (2)
- The dimension of harmonic measure on some AD-regular flat sets of fractional dimension (2023) (1)
- Principal values for the Cauchy transform and rectifiability (2014) (1)
- E'S PROBLEM AND ANALYTIC CAPACITY (2004) (1)
- On $$C^1$$C1-approximability of functions by solutions of second order elliptic equations on plane compact sets and C-analytic capacity (2018) (1)
- NON-EXISTENCE OF REFLECTIONLESS MEASURES FOR THE s-RIESZ TRANSFORM WHEN 0 < s < 1 (2015) (1)
- Characterization of n-rectifiability in terms of Jones’ square function: Part II (2015) (1)
- About the Jones-Wolff Theorem on the Hausdorff dimension of harmonic measure (2018) (1)
- Solvability of the Poisson-Dirichlet problem with interior data in $L^{p'}$-Carleson spaces and its applications to the $L^{p}$-regularity problem (2022) (1)
- The Riesz transform and quantitative rectifiability for general Radon measures (2017) (1)
- The two-phase problem for harmonic measure in VMO (2020) (1)
- Characterization of n-rectifiability in terms of Jones’ square function: part I (2015) (0)
- Basic Calderón-Zygmund theory with non-doubling measures (2014) (0)
- Harmonic measure and quantitative connectivity: geometric characterization of the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \beg (2020) (0)
- The $A_\infty$ condition, $\varepsilon$-approximators, and Varopoulos extensions in uniform domains (2023) (0)
- Strong and weak type estimates for singular integrals with respect to measures separated by AD-regular boundaries (2013) (0)
- Rectifiability of harmonic measure (2016) (0)
- RBMO (μ) and \( {H}_{atb}^{1}(\mu)\) (2014) (0)
- Capacities associated with Calder\'on-Zygmund kernels (2011) (0)
- LIPSCHITZ HARMONIC CAPACITY , BILIPSCHITZ IMAGES OF CANTOR SETS 21 Case (2006) (0)
- Capacities Associated with Calderón-Zygmund Kernels (2012) (0)
- Weighted norm inequalities for Calderón-Zygmund operators (2007) (0)
- A Tb theorem of Nazarov, Treil and Volberg (2014) (0)
- The Cauchy transform and Menger curvature (2014) (0)
- A proof of Carleson's $\varepsilon^2$-conjecture (2019) (0)
- Riesz Transforms and Rectifiability (2009) (0)
- Correction to: Characterization of n-rectifiability in terms of Jones’ square function: part I (2019) (0)
- $$L^2$$-Boundedness of Gradients of Single Layer Potentials for Elliptic Operators with Coefficients of Dini Mean Oscillation-Type (2021) (0)
- Curvature and rectifiability (2014) (0)
- The comparability between γ and γ+, and the semiadditivity of analytic capacity (2014) (0)
- Mass Transport and Uniform Rectifiability (2012) (0)
- Correction to: Characterization of n-rectifiability in terms of Jones’ square function: part I (2019) (0)
- A family of singular integral operators which control the Cauchy transform (2019) (0)
- A dual characterization of the ${\mathcal C}^{1}$ harmonic capacity and applications (2009) (0)
- Within the conference there will be plenary talks and minisymposia on special topics. Every participant can also give a contributed talk or present a poster. (2013) (0)
- Connectivity conditions and boundary Poincar\'e inequalities (2022) (0)
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