S. Hofmann

发表

The Solution of the Kato Problem for Divergence Form Elliptic Operators with Gaussian Heat Kernel Bounds

M. Lacey, S. Hofmann, A. Mcintosh, 2002 .

Extrapolation of Carleson measures and the analyticity of Kato's square-root operators

John L. Lewis, Pascal Auscher, Philippe Tchamitchian, 2001 .

Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains

Michael E. Taylor, M. Mitrea, S. Hofmann, 2007 .

$L^2$ solvability and representation by caloric layer potentials in time-varying domains

John L. Lewis, S. Hofmann, 1996 .

Nontangential Estimates on Layer Potentials and the Neumann Problem for Higher-Order Elliptic Equations

S. Mayboroda, S. Hofmann, A. Barton, 2018, International Mathematics Research Notices.

FOURIER TRANSFORM OF A BOUNDED SET

S. Hofmann, L. Brandolini, A. Iosevich, 2003 .

Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations

Andrew J. Morris, S. Hofmann, P. Le, 2017, Analysis & PDE.

Uniform Rectifiability and harmonic measure IV: Ahlfors regularity plus Poisson kernels in $L^p$ implies uniform rectifiability

S. Hofmann, J. M. Martell, 2015, 1505.06499.

The solution of the Kato problem in two dimensions

S. Hofmann, A. Mcintosh, 2002 .

THE KATO SQUARE ROOT PROBLEM ON AN ARBITRARY DOMAIN OF R d

R. Coifman, P. Tchamitchian, A., 2020 .

Tl THEOREMS FOR BESOV AND TRIEBEL-LIZORKIN SPACES

S. Hofmann, 2010 .

Riesz transform on manifolds and heat kernel regularity

P. Auscher, S. Hofmann, X. Duong, 2004, math/0411374.

Critical perturbations for second-order elliptic operators, I: Square function bounds for layer potentials

S. Mayboroda, S. Hofmann, J. García, 2020, Analysis & PDE.

A weak molecule condition for certain Triebel-Lizorkin spaces

S. Hofmann, 1992 .

The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients

C. Kenig, J. Pipher, S. Mayboroda, 2014, Mathematische Annalen.

Quantitative Fatou Theorems and Uniform Rectifiability

S. Hofmann, S. Bortz, 2019, Potential Analysis.

Carleson measures, trees, extrapolation, and T(b) theorems

T. Tao, P. Auscher, C. Thiele, 2001, math/0108138.

On singular integrals of Calderón-type in Rn and BMO

S. Hofmann, 1994 .

Corona Decompositions for Parabolic Uniformly Rectifiable Sets

S. Hofmann, K. Nystrom, J. García, 2021, 2103.12497.

Rectifiability of harmonic measure

X. Tolsa, A. Volberg, S. Mayboroda, 2016, Geometric and Functional Analysis.

Rectifiability of harmonic measure

X. Tolsa, A. Volberg, S. Mayboroda, 2015, 1509.06294.

Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus

M. Mitrea, S. Hofmann, Michael Taylor, 2015 .

Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains

M. Mitrea, S. Hofmann, Michael Taylor, 2009 .

Absolute continuity between the surface measure and harmonic measure implies rectifiability

X. Tolsa, A. Volberg, S. Mayboroda, 2015, 1507.04409.

On big pieces approximations of parabolic hypersurfaces

Simon Bortz, John Hoffman, Steve Hofmann, 2021, Annales Fennici Mathematici.

Parabolic Singular Integrals with Nonhomogeneous Kernels

Simon Bortz, John Hoffman, Steve Hofmann, 2021, 2103.12830.

Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets

Simon Bortz, John Hoffman, Steve Hofmann, 2021, 2103.12502.

Uniform rectifiability implies Varopoulos extensions

S. Hofmann, Olli Tapiola, 2020, 2003.07749.

A∞ implies NTA for a class of variable coefficient elliptic operators

S. Hofmann, T. Toro, J. M. Martell, 2016, 1611.09561.

GENERALIZED LOCAL THEOREMS FOR SQUARE FUNCTIONS

S. Hofmann, Ana Grau de la Herrán, Ana Grau de la Herran, 2012, 1212.5870.

Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries

S. Hofmann, Matthew Badger, J. M. Martell, 2015, 1507.02039.

Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains

F. Gesztesy, S. Hofmann, Roger Nichols, 2014, 1411.4789.

The method of layer potentials in Lp and endpoint spaces for elliptic operators with L∞ coefficients

Andrew J. Morris, M. Mitrea, S. Hofmann, 2013, 1311.4783.

$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

Andrew J. Morris, M. Mitrea, S. Hofmann, 2013, 1301.4943.

On Stability of Square Root Domains for Non-Self-Adjoint Operators Under Additive Perturbations

F. Gesztesy, S. Hofmann, Roger Nichols, 2012, 1212.5661.

Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$

S. Hofmann, J. M. Martell, 2012, 1202.3857.

Vertical versus conical square functions

P. Auscher, S. Hofmann, J. M. Martell, 2010, 1012.4184.

Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates

M. Mitrea, S. Hofmann, D. Mitrea, 2011 .

Boundedness and applications of singular integrals and square functions: a survey

S. Hofmann, A. Mcintosh, 2011 .

Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients

P. Auscher, S. Hofmann, A. Axelsson, 2007, 0705.0836.

Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces

S. Mayboroda, S. Hofmann, A. Mcintosh, 2010, 1002.0792.

Hardy and BMO spaces associated to divergence form elliptic operators

S. Mayboroda, S. Hofmann, 2006, math/0611804.

Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains

John L. Lewis, M. Mitrea, S. Hofmann, 2003 .

Sharp rate of average decay of the Fourier transform of a bounded set

A. Iosevich, S. Hofmann, L. Brandolini, 2003, math/0303188.

APPENDIX THE MARY WEISS LEMMA

L. Grafakos, S. Hofmann, 2003 .

Dirichlet problems for a nonstationary linearized system of Navier–Stokes equations in non-cylindrical domains

K. Nyström, S. Hofmann, 2002 .

The Dirichlet problem for parabolic operators with singular drift terms

John L. Lewis, S. Hofmann, 2001 .

A Generalized Characterization of Commutators of Parabolic Singular Integrals

S. Hofmann, Dachun Yang, Xinwei Li, 1999, Canadian Mathematical Bulletin.

A note on weighted Sobolev spaces, and regularity of commutators and layer potentials associated to the heat equation

S. Hofmann, 1993 .

Singular integrals with power weights

S. Hofmann, 1990 .

Weighted weak-type (1,1) inequalities for rough operators

S. Hofmann, 1989 .

Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

M. Mitrea, S. Hofmann, Sylvie Monniaux, 2011 .

Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition

S. Hofmann, T. Toro, J. M. Martell, 2019, Forum Mathematicum.

Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition

Zihui Zhao, S. Mayboroda, S. Hofmann, 2017, Geometric and Functional Analysis.

Harmonic measure and quantitative connectivity: geometric characterization of the $$L^p$$-solvability of the Dirichlet problem

S. Hofmann, J. M. Martell, 2017, Inventiones mathematicae.

Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates

S. Hofmann, T. Toro, J. Cavero, 2019, 1908.02268.

Quantitative Fatou Theorems and Uniform Rectifiability

S. Hofmann, S. Bortz, 2018, Potential Analysis.

Uniform rectifiability and ε-approximability of harmonic functions in L p

S. Hofmann, Olli Tapiola, 2017, Annales de l'Institut Fourier.

The weak-A∞ property of harmonic and p-harmonic measures implies uniform rectifiability

S. Hofmann, K. Nystrom, J. M. Martell, 2015, 1511.09270.

BMO Solvability and Absolute Continuity of Harmonic Measure

S. Hofmann, Phi Le, 2016, 1607.00418.

Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions

S. Mayboroda, S. Hofmann, J. M. Martell, 2014, 1408.1447.

Uniform rectifiability and harmonic measure, II: Poisson kernels in $L^{p}$ imply uniform rectifiability

S. Hofmann, I. Uriarte-Tuero, J. M. Martell, 2012, 1202.3860.

Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators

C. Kenig, J. Pipher, S. Mayboroda, 2012, 1202.2405.

The Green function estimates for strongly elliptic systems of second order

S. Hofmann, Seick Kim, 2007, 0704.1352.

Dirichlet and Neumann boundary values of solutions to higher order elliptic equations

S. Mayboroda, S. Hofmann, Ariel Barton, 2017, Annales de l'Institut Fourier.

The solution of the Kato square root problem for second order elliptic operators on Rn

Pascal Auscher, Michael T. Lacey, Philippe Tchamitchian, 2002 .

A local Tb Theorem for square functions

S. Hofmann, 2011 .

The commutator of the Kato square root for second order elliptic operators on ℝn

S. Hofmann, Yong Ding, Y. Chen, 2016, Acta Mathematica Sinica, English Series.

The commutator of the Kato square root for second order elliptic operators on ℝn

S. Hofmann, Yong Ding, Y. Chen, 2016 .

Local Tb theorems and applications in PDE

S. Hofmann, 2006 .

Integral operators and weighted amalgams

S. Hofmann, H. P. Heinig, C. Carton-Lebrun, 1994 .

Weighted norm inequalities and vector valued inequalities for certain rough operators

S. Hofmann, 1993 .

Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems

Dorina Mitrea, Marius Mitrea, Xuan Thinh Duong, 2013 .

A proof of the local $Tb$ Theorem for standard Calder\'{o}n-Zygmund operators

S. Hofmann, 2007, 0705.0840.

Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition

Steve Hofmann, Murat Akman, Jos'e Mar'ia Martell, 2021, Advances in Calculus of Variations.

Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators

S. Hofmann, J. Cavero, J. M. Martell, 2017, Transactions of the American Mathematical Society.

A new characterization of chord-arc domains

S. Hofmann, K. Nystrom, T. Toro, 2014, 1406.2743.

Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains

S. Mayboroda, S. Hofmann, J. M. Martell, 2019, 1904.13116.

_{∞} estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators

S. Hofmann, J. M. Martell, 2012 .

Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems

P. Auscher, S. Hofmann, A. Axelsson, 2007, 0705.0250.

Hardy Spaces, Singular Integrals and The Geometry of Euclidean Domains of Locally Finite Perimeter

M. Mitrea, S. Hofmann, S. Pérez-Esteva, 2009 .

Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure

X. Tolsa, A. Volberg, S. Mayboroda, 2015, 1509.06558.

The Neumann problem for higher order elliptic equations with symmetric coefficients

S. Mayboroda, S. Hofmann, Ariel Barton, 2017, Mathematische Annalen.

Corona Decompositions for Parabolic Uniformly Rectifiable Sets

K. Nyström, S. Hofmann, S. Bortz, 2021, The Journal of Geometric Analysis.

Coronizations and big pieces in metric spaces

S. Hofmann, K. Nystrom, J. García, 2020, Annales de l'Institut Fourier.

Caloric measure in parabolic flat domains

John L. Lewis, K. Nyström, S. Hofmann, 2004 .

EXISTENCE OF BIG PIECES OF GRAPHS FOR PARABOLIC PROBLEMS

John L. Lewis, K. Nyström, S. Hofmann, 2003 .

Square function estimates on layer potentials for higher‐order elliptic equations

S. Mayboroda, S. Hofmann, Ariel Barton, 2015, 1508.04988.

THE T (b) THEOREM AND ITS VARIANTS

T. Tao, C. Thiele, S. Hofmann, 2003 .

On square root domains for non-self-adjoint Sturm-Liouville operators

F. Gesztesy, S. Hofmann, Roger Nichols, 2013, 1305.2650.

Quantitative Absolute Continuity of Harmonic Measure and the Dirichlet Problem: A Survey of Recent Progress

S. Hofmann, 2019, Acta Mathematica Sinica, English Series.

Quantitative Absolute Continuity of Harmonic Measure and the Dirichlet Problem: A Survey of Recent Progress

S. Hofmann, 2019, Acta Mathematica Sinica, English Series.

A singular integral approach to a two phase free boundary problem

S. Hofmann, S. Bortz, 2015, 1505.05419.

Kato square root problem with unbounded leading coefficients

S. Hofmann, L. Escauriaza, 2017, Proceedings of the American Mathematical Society.

The solution of Kato's conjectures

John L. Lewis, P. Tchamitchian, P. Auscher, 2001 .

The Kato square root problem for higher order elliptic operators and systems on $ \Bbb R^n $

Pascal Auscher, Philippe Tchamitchian, Steve Hofmann, 2001 .

Rectifiability, interior approximation and harmonic measure

S. Hofmann, J. M. Martell, S. Bortz, 2016, Arkiv för Matematik.

C A ] 9 O ct 2 01 8 RECTIFIABILITY , INTERIOR APPROXIMATION AND HARMONIC MEASURE

S. Hofmann, J. M. Martell, S. Bortz, 2020 .

Gaussian estimates for fundamental solutions to certain parabolic systems.

S. Hofmann, Seick Kim, 2004 .

On the Kato problem for elliptic operators in non-divergence form

S. Hofmann, L. Escauriaza, Pablo Hidalgo-Palencia, 2023, 2304.14694.

The Dirichlet problem for elliptic operators having a BMO anti-symmetric part

J. Pipher, S. Mayboroda, S. Hofmann, 2019, Mathematische Annalen.

$$L^p$$ theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part

Jill Pipher, Svitlana Mayboroda, Steve Hofmann, 2019, Mathematische Zeitschrift.

The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients

C. Kenig, J. Pipher, S. Mayboroda, 2013, 1301.5209.

Bounds on layer potentials with rough inputs for higher order elliptic equations

S. Mayboroda, S. Hofmann, Ariel Barton, 2017, Proceedings of the London Mathematical Society.

Lp bounds for Riesz transforms and square roots associated to second order elliptic operators

S. Hofmann, J. M. Martell, 2003 .

A sufficient geometric criterion for quantitative absolute continuity of harmonic measure

S. Hofmann, J. M. Martell, 2017 .

A Weak Reverse Hölder Inequality for Caloric Measure

S. Hofmann, Alyssa Genschaw, 2019, Journal of Geometric Analysis.

A Weak Reverse Hölder Inequality for Caloric Measure

S. Hofmann, Alyssa Genschaw, 2018, The Journal of Geometric Analysis.

Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics

Alex Iosevich, Steve Hofmann, S. Hofmann, 2004 .

The $L^{p}$ regularity problem for the heat equation in non-cylindrical domains

John L. Lewis, S. Hofmann, 1999 .

BMO Solvability and Absolute Continuity of Caloric Measure

S. Hofmann, Alyssa Genschaw, 2019, Potential Analysis.

Weak (1,1) boundedness of singular integrals with nonsmooth kernel

S. Hofmann, 1988 .

Gaussian estimates for fundamental solutions to certain parabolic systems.

S. Hofmann, Seick Kim, 2004 .

The ${L}^p$ Neumann problem for the heat equation in non-cylindrical domains

John L. Lewis, S. Hofmann, 1998 .

The Neumann problem for higher order elliptic equations with symmetric coefficients

S. Mayboroda, S. Hofmann, Ariel Barton, 2017, Mathematische Annalen.

Layer potentials and boundary value problems for elliptic equations with complex $L^{\infty}$ coefficients satisfying the small Carleson measure norm condition

S. Mayboroda, S. Hofmann, Mihalis Mourgoglou, 2013, 1311.0086.

Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets

S. Hofmann, K. Nystrom, J. García, 2021, Analysis & PDE.

Uniform Rectifiability and Elliptic Operators Satisfying a Carleson Measure Condition

Zihui Zhao, S. Mayboroda, S. Hofmann, 2020, Geometric and Functional Analysis.

BOUND CRITERION FOR SINGULAR INTEGRALS WITH ROUGH KERNEL AND ITS APPLICATIONS

F. Soria, S. Hofmann, A. Seeger, 2018 .

Lattice points inside random ellipsoids

S. Hofmann, A. Iosevich, D. Weidinger, 2004 .

FALCONER CONJECTURE IN THE PLANE FOR RANDOM METRICS

S. Hofmann, A. Iosevich, 2003, math/0305132.