Steve Hofmann | Academic Influence

Steve Hofmann's AcademicInfluence.com Rankings

Steve Hofmann

Mathematics

#1493

World Rank

#2441

Historical Rank

#614

USA Rank

Measure Theory

#3403

World Rank

#4018

Historical Rank

#984

USA Rank

mathematics Degrees

Download Badge

Mathematics

Steve Hofmann's Degrees

Masters Mathematics Stanford University
Bachelors Mathematics Princeton University

Similar Degrees You Can Earn

Best Online Bachelor's in Math 2025

Why Is Steve Hofmann Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Steve Hofmann is a mathematician who helped solve the famous Kato's conjecture. Said Hofmann, “It's a problem that has interested me since I was a graduate student... It was one of the biggest open problems in my field and everybody thought it was too hard and wouldn't be solved. I had toyed with it for years and then put in three years of very serious work before hitting the key breakthrough.”

(See a Problem?)

Steve Hofmann'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

The solution of the Kato square root problem for second order elliptic operators on Rn (2002) (352)
Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates (2011) (313)
Riesz transform on manifolds and heat kernel regularity (2004) (275)
Hardy and BMO spaces associated to divergence form elliptic operators (2006) (265)
Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces (2010) (160)
The Green function estimates for strongly elliptic systems of second order (2007) (129)
Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains (2009) (122)
Lp bounds for Riesz transforms and square roots associated to second order elliptic operators (2003) (115)
Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators (2012) (103)
Carleson measures, trees, extrapolation, and T(b) theorems (2001) (101)
Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients (2007) (96)
The Kato square root problem for higher order elliptic operators and systems on $ \Bbb R^n $ (2001) (90)
Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains (2007) (90)
Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$ (2012) (90)
Extrapolation of Carleson measures and the analyticity of Kato's square-root operators (2001) (88)
$L^2$ solvability and representation by caloric layer potentials in time-varying domains (1996) (82)
A new characterization of chord-arc domains (2014) (78)
The Solution of the Kato Problem for Divergence Form Elliptic Operators with Gaussian Heat Kernel Bounds (2002) (77)
The Dirichlet problem for parabolic operators with singular drift terms (2001) (72)
Rectifiability of harmonic measure (2015) (71)
Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems (2007) (68)
Uniform rectifiability and harmonic measure, II: Poisson kernels in $L^{p}$ imply uniform rectifiability (2012) (66)
Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials (1997) (58)
Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions (2014) (54)
The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients (2013) (52)
Sharp rate of average decay of the Fourier transform of a bounded set (2003) (51)
Harmonic measure and quantitative connectivity: geometric characterization of the $$L^p$$-solvability of the Dirichlet problem (2017) (49)
The weak-A∞ property of harmonic and p-harmonic measures implies uniform rectifiability (2015) (49)
Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics (2004) (49)
The method of layer potentials in Lp and endpoint spaces for elliptic operators with L∞ coefficients (2013) (48)
Weak (1,1) boundedness of singular integrals with nonsmooth kernel (1988) (46)
Weighted norm inequalities and vector valued inequalities for certain rough operators (1993) (45)
The solution of the Kato problem in two dimensions (2002) (44)
Caloric measure in parabolic flat domains (2004) (42)
Vertical versus conical square functions (2010) (41)
$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets (2013) (37)
A∞ implies NTA for a class of variable coefficient elliptic operators (2016) (35)
Layer potentials and boundary value problems for elliptic equations with complex $L^{\infty}$ coefficients satisfying the small Carleson measure norm condition (2013) (34)
On certain nonstandard Calderón-Zygmund operators (1994) (33)
Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in $L^p$ implies uniform rectifiability (2015) (32)
Gaussian estimates for fundamental solutions to certain parabolic systems. (2004) (31)
Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries (2015) (29)
Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains (2012) (28)
EXISTENCE OF BIG PIECES OF GRAPHS FOR PARABOLIC PROBLEMS (2003) (27)
Local Tb theorems and applications in PDE (2006) (27)
BMO Solvability and Absolute Continuity of Harmonic Measure (2016) (26)
The solution of Kato's conjectures (2001) (26)
Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition (2017) (26)
A local Tb Theorem for square functions (2011) (24)
A proof of the local $Tb$ Theorem for standard Calder\'{o}n-Zygmund operators (2007) (23)
Hardy Spaces, Singular Integrals and The Geometry of Euclidean Domains of Locally Finite Perimeter (2009) (22)
Square function estimates on layer potentials for higher‐order elliptic equations (2015) (20)
_{∞} estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators (2012) (19)
On singular integrals of Calderón-type in Rn and BMO (1994) (18)
The Lp Neumann problem for the heat equation in non-cylindrical domains (2005) (18)
Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains (2019) (17)
Harmonic measure and approximation of uniformly rectifiable sets (2015) (17)
Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus (2015) (17)
Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates (2019) (16)
The $L^{p}$ regularity problem for the heat equation in non-cylindrical domains (1999) (16)
Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems (2013) (16)
Boundedness and applications of singular integrals and square functions: a survey (2011) (15)
Square functions of Calderón type and applications (2001) (15)
Integral operators and weighted amalgams (1994) (14)
An Off-DiagonalT1 Theorem and Applications (1998) (14)
The ${L}^p$ Neumann problem for the heat equation in non-cylindrical domains (1998) (13)
Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators (2017) (13)
Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains (2003) (11)
Dahlberg’s bilinear estimate for solutions of divergence form complex elliptic equations (2007) (11)
Weighted weak-type (1,1) inequalities for rough operators (1989) (11)
Rectifiability, interior approximation and harmonic measure (2016) (11)
Boundedness Criteria for Rough Singular Integrals (1995) (10)
Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations (2017) (10)
Kato square root problem with unbounded leading coefficients (2017) (9)
Absolute continuity between the surface measure and harmonic measure implies rectifiability (2015) (9)
On Stability of Square Root Domains for Non-Self-Adjoint Operators Under Additive Perturbations (2012) (9)
Dirichlet and Neumann boundary values of solutions to higher order elliptic equations (2017) (8)
Bounds on layer potentials with rough inputs for higher order elliptic equations (2017) (8)
Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition (2019) (8)
Uniform rectifiability and elliptic operators with small Carleson norm (2017) (8)
A singular integral approach to a two phase free boundary problem (2015) (8)
A Weak Reverse Hölder Inequality for Caloric Measure (2018) (8)
Lattice points inside random ellipsoids (2004) (8)
Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds (2011) (8)
Singular integrals with power weights (1990) (7)
Quantitative Absolute Continuity of Harmonic Measure and the Dirichlet Problem: A Survey of Recent Progress (2019) (7)
Coronizations and big pieces in metric spaces (2020) (7)
Nontangential Estimates on Layer Potentials and the Neumann Problem for Higher-Order Elliptic Equations (2018) (6)
A sufficient geometric criterion for quantitative absolute continuity of harmonic measure (2017) (6)
Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains (2014) (6)
The Dirichlet problem for elliptic operators having a BMO anti-symmetric part (2019) (6)
Dirichlet problems for a nonstationary linearized system of Navier–Stokes equations in non-cylindrical domains (2002) (6)
The commutator of the Kato square root for second order elliptic operators on ℝn (2016) (6)
Critical perturbations for second-order elliptic operators, I: Square function bounds for layer potentials (2020) (5)
Uniform rectifiability and ε-approximability of harmonic functions in L p (2017) (5)
A weak molecule condition for certain Triebel-Lizorkin spaces (1992) (5)
Quantitative Fatou Theorems and Uniform Rectifiability (2018) (5)
Corona Decompositions for Parabolic Uniformly Rectifiable Sets (2021) (4)
Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure (2015) (4)
Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition (2021) (4)
The Calderón commutator along a parabola (1997) (4)
On big pieces approximations of parabolic hypersurfaces (2021) (4)
Square Function Estimates in Spaces of Homogeneous Type and on Uniformly Rectifiable Euclidean Sets (2014) (4)
A Generalized Characterization of Commutators of Parabolic Singular Integrals (1999) (3)
On square root domains for non-self-adjoint Sturm-Liouville operators (2013) (3)
A note on weighted Sobolev spaces, and regularity of commutators and layer potentials associated to the heat equation (1993) (3)
GENERALIZED LOCAL THEOREMS FOR SQUARE FUNCTIONS (2012) (3)
$$L^p$$ theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part (2019) (3)
Regularity and Neumann problems for operators with real coefficients satisfying Carleson condition (2022) (3)
L2 estimates for commutators of the Dirichlet-to-Neumann Map associated to elliptic operators with complex-valued bounded measurable coefficients on R+n+1 (2021) (3)
Uniform rectifiability implies Varopoulos extensions (2020) (3)
BMO Solvability and Absolute Continuity of Caloric Measure (2019) (3)
FALCONER CONJECTURE IN THE PLANE FOR RANDOM METRICS (2003) (2)
THE KATO SQUARE ROOT PROBLEM ON AN ARBITRARY DOMAIN OF R d (2020) (2)
Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets (2021) (2)
Real Harmonic Analysis and its Applications to Partial Differential Equations and Geometric Measure Theory (2018) (1)
FOURIER TRANSFORM OF A BOUNDED SET (2003) (1)
The Neumann problem for higher order elliptic equations with symmetric coefficients (2017) (1)
BMO Solvability and Absolute Continuity of Harmonic Measure (2017) (0)
Quantitative Rectifiability and Elliptic Equations (2014) (0)
BOUND CRITERION FOR SINGULAR INTEGRALS WITH ROUGH KERNEL AND ITS APPLICATIONS (2018) (0)
Quantitative Absolute Continuity of Harmonic Measure and the Dirichlet Problem: A Survey of Recent Progress (2019) (0)
Boundary problems for the second order elliptic equations with rough coefficients (2010) (0)
PROCEEDINGS OF THE INTERNET ANALYSIS SEMINAR ON: RIESZ TRANSFORMS ASSOCIATED TO SCHRÖDINGER OPERATORS (2015) (0)
THE T (b) THEOREM AND ITS VARIANTS (2003) (0)
Parabolic Singular Integrals with Nonhomogeneous Kernels (2021) (0)
Rectifiability of harmonic measure (2016) (0)
ON COMMUTATOR ALONG A PARABOLA (1997) (0)
Tl THEOREMS FOR BESOV AND TRIEBEL-LIZORKIN SPACES (2010) (0)
Correction to: A Weak Reverse Hölder Inequality for Caloric Measure (2022) (0)
APPENDIX THE MARY WEISS LEMMA (2003) (0)
Correction to: A Weak Reverse Hölder Inequality for Caloric Measure (2022) (0)
The commutator of the Kato square root for second order elliptic operators on ℝn (2016) (0)
T1 and Tb theorems and applications (2020) (0)
Critical Perturbations for Second Order Elliptic Operators. Part II: Non-tangential maximal function estimates (2023) (0)
Calori Measure in Paraboli Flat Domains (2007) (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)
A Weak Reverse Hölder Inequality for Caloric Measure (2019) (0)
J un 2 01 4 A NEW CHARACTERIZATION OF CHORD-ARC DOMAINS (0)
On the Kato problem for elliptic operators in non-divergence form (2023) (0)
The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients (2014) (0)
A note on $A_\infty$ Estimates Via Extrapolation of Carleson Measures (2010) (0)
Quantitative Fatou Theorems and Uniform Rectifiability (2019) (0)
The Dirichlet problem for elliptic operators having a BMO anti-symmetric part (2021) (0)
C A ] 9 O ct 2 01 8 RECTIFIABILITY , INTERIOR APPROXIMATION AND HARMONIC MEASURE (2020) (0)

This paper list is powered by the following services:

Other Resources About Steve Hofmann

en.wikipedia.org

What Schools Are Affiliated With Steve Hofmann?

Steve Hofmann is affiliated with the following schools: