Michael Lacey | Academic Influence

Michael Lacey 's AcademicInfluence.com Rankings

Michael Lacey

Mathematics

#679

World Rank

#1244

Historical Rank

#298

USA Rank

Geometry

#74

World Rank

#125

Historical Rank

#19

USA Rank

Measure Theory

#945

World Rank

#1231

Historical Rank

#352

USA Rank

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Mathematics

Michael Lacey 's Degrees

Bachelors Mathematics University of Texas at Austin

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Why Is Michael Lacey Influential?

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According to Wikipedia, Michael Thoreau Lacey is an American mathematician. Lacey received his PhD from the University of Illinois at Urbana-Champaign in 1987, under the direction of Walter Philipp. His thesis was in the area of probability in Banach spaces, and solved a problem related to the law of the iterated logarithm for empirical characteristic functions. In the intervening years, his work has touched on the areas of probability, ergodic theory, and harmonic analysis.

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Michael Lacey '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)
On Calderon s conjecture (1999) (343)
$L^p$ estimates on the bilinear Hilbert transform for $2 < p < \infty$ (1997) (255)
A note on the almost sure central limit theorem (1990) (237)
An elementary proof of the A2 bound (2015) (194)
A proof of boundedness of the Carleson operator (2000) (175)
Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, II (2012) (139)
Sharp weighted bounds for the q‐variation of singular integrals (2012) (124)
On the Small Ball Inequality in All Dimensions (2007) (116)
Sharp A2 inequality for Haar shift operators (2009) (114)
SHARP WEIGHTED BOUNDS FOR FRACTIONAL INTEGRAL OPERATORS (2009) (110)
Commutators in the two-weight setting (2015) (104)
The bilinear maximal functions map into L^p for 2/3 < p <= 1 (2000) (101)
On Calder\'on's conjecture (1999) (90)
Two Weight Inequalities for Discrete Positive Operators (2009) (89)
A characterization of productBMO by commutators (2002) (80)
The Solution of the Kato Problem for Divergence Form Elliptic Operators with Gaussian Heat Kernel Bounds (2002) (77)
On the small ball inequality in three dimensions (2006) (72)
Sparse bounds for spherical maximal functions (2017) (63)
Maximal theorems for the directional Hilbert transform on the plane (2003) (60)
Hankel Operators in Several Complex Variables and Product $BMO\zProd$ (2003) (60)
L(p) estimates for the bilinear Hilbert transform. (1997) (59)
Borderline weak‐type estimates for singular integrals and square functions (2015) (55)
Breaking the duality in the return times theorem (2006) (54)
The A_p-A_infty inequality for general Calderon--Zygmund operators (2011) (51)
L P Estimates on the Bilinear Hilbert Transform for 2 < P < 1 (1997) (48)
On the bilinear Hilbert transform. (1998) (48)
A Two Weight Inequality for the Hilbert transform Assuming an Energy Hypothesis (2010) (46)
On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields (2007) (45)
Issues related to Rubio de Francia's Littlewood--Paley Inequality: A Survey (2003) (45)
Carleson's Theorem: Proof, Complements, Variations (2003) (44)
Paraproducts in one and several parameters (2005) (41)
Weak and strong type estimates for maximal truncations of Calderón-Zygmund operators on Ap weighted spaces (2011) (40)
The Sparse T1 Theorem (2016) (40)
Bloom’s inequality: commutators in a two-weight setting (2015) (39)
Sparse Bounds for Oscillatory and Random Singular Integrals (2016) (36)
Weak And Strong Type Estimates for Maximal Truncations of Calder\'on-Zygmund Operators on $ A_p$ Weighted Spaces (2011) (35)
On Calderón's conjecture for the bilinear Hilbert transform. (1998) (35)
Pointwise convergence of vector-valued Fourier series (2012) (34)
Sparse bounds for the discrete cubic Hilbert transform (2016) (34)
A note on the almost everywhere central limit theorem (1989) (33)
A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure (2008) (32)
The Two Weight Inequality for the Hilbert Transform: A Primer (2013) (29)
Exponential Squared Integrability for the Discrepancy Function in Two Dimensions (2008) (28)
On bilinear Littlewood-Paley square functions (1996) (28)
The solution of Kato's conjectures (2001) (26)
Variations on the Theme of Journe's Lemma (2004) (26)
A Wiener–Wintner theorem for the Hilbert transform (2008) (26)
On the Separated Bumps Conjecture for Calderon-Zygmund Operators (2013) (25)
Sparse Bounds for Bochner–Riesz Multipliers (2017) (25)
Iterated Riesz Commutators: A Simple Proof of Boundedness (2008) (25)
Astala’s conjecture on distortion of Hausdorff measures under quasiconformal maps in the plane (2008) (25)
Two weight norm inequalities for the $g$ function (2013) (24)
Two Weight Inequalities for Riesz Transforms: Uniformly Full Dimension Weights (2013) (23)
Sparse Bounds for Random Discrete Carleson Theorems (2016) (23)
Lectures on Nehari's Theorem on the Polydisk (2006) (22)
Random ergodic theorems with universally representative sequences (1994) (21)
One-bit sensing, discrepancy and Stolarsky's principle (2015) (21)
On central limit theorems, modulus of continuity and diophantine type for irrational rotations (1993) (21)
Weighted bounds for variational Fourier series (2012) (21)
Local $Tb$ theorem with $L^2$ testing conditions and general measures: Calder\'on-Zygmund operators (2013) (21)
Remarks on Product VMO (2004) (21)
Commutators with Reisz potentials in one and several parameters (2005) (20)
On sets of integers not containing long arithmetic progressions (2001) (19)
The Two Weight Inequality for Hilbert Transform, Coronas, and Energy Conditions (2011) (19)
C V ] 1 5 A pr 2 01 4 TWO WEIGHT INEQUALITIES FOR THE CAUCHY TRANSFORM FROM R TO C + (2014) (19)
Two Weight Inequalities for the Cauchy Transform from $ \mathbb{R}$ to $ \mathbb{C}_+$ (2013) (18)
On the convergence of lacunary Walsh–Fourier series (2011) (17)
Large Deviations for the Maximum Local Time of Stable Levy Processes (1990) (17)
The Supremum Norm of the Discrepancy Function: Recent Results and Connections (2012) (17)
RIESZ BASES OF EXPONENTIALS ON MULTIBAND SPECTRA (2012) (17)
Sparse endpoint estimates for Bochner–Riesz multipliers on the plane (2017) (16)
On Entropy Bumps for Calderón-Zygmund Operators (2015) (16)
On A p – A ∞ type estimates for square functions (2016) (16)
Weighted Weak Type Estimates for Square Functions (2012) (16)
ℓp-Improving Inequalities for Discrete Spherical Averages (2020) (16)
On $$A_p$$Ap–$$A_\infty $$A∞ type estimates for square functions (2015) (16)
Local Tb theorem with L2 testing conditions and general measures: square functions (2013) (16)
Random Tessellations, Restricted Isometric Embeddings, and One Bit Sensing (2015) (15)
COMMUTATORS OF WEIGHTED HARDY OPERATORS ON R (2009) (15)
On weak convergence in dynamical systems to self-similar processes with spectral representation (1991) (15)
A VARIATION NORM CARLESON THEOREM FOR VECTOR-VALUED WALSH-FOURIER SERIES (2012) (15)
Carleson's theorem with quadratic phase functions (2002) (14)
Multi‐parameter Div–Curl lemmas (2010) (14)
A Discrete Quadratic Carleson Theorem on with ℓ2 a Restricted Supremum (2016) (14)
The vector valued quartile operator (2012) (14)
On the Signed Small Ball Inequality (2007) (14)
Sparse bounds for the discrete spherical maximal functions (2018) (13)
$ \ell ^{p}$-improving inequalities for Discrete Spherical Averages (2018) (13)
A weak–type orthogonality principle (2002) (13)
On an Argument of Shkredov on Two-Dimensional Corners (2005) (12)
Weak and Strong type $ A_p$ Estimates for Calderón-Zygmund Operators (2010) (12)
Sparse bounds for maximally truncated oscillatory singular integrals (2017) (12)
Compactness of commutator of Riesz transforms in the two weight setting (2020) (12)
Weak and Strong-type estimates for Haar Shift Operators: Sharp power on the $A_p$ characteristic (2009) (12)
Pointwise convergence of Walsh--Fourier series of vector-valued functions (2012) (12)
Limit laws for local times of the Brownian sheet (1990) (11)
A THREE DIMENSIONAL SIGNED SMALL BALL INEQUALITY (2009) (10)
Lacunary Discrete Spherical Maximal Functions (2018) (10)
Averages Along the Primes: Improving and Sparse Bounds (2019) (10)
Weighted Bounds for Variational Walsh–Fourier Series (2011) (10)
PACKING SPHERES AND FRACTAL STRICHARTZ ESTIMATES IN R FOR d ≥ 3 (2006) (10)
On the discrepancy function in arbitrary dimension, close to L1 (2008) (10)
A Discrete Quadratic Carleson Theorem on $ \ell ^2 $ with a Restricted Supremum (2015) (10)
Ergodic averages on circles (1995) (10)
A remark on the multiparameter law of the iterated logarithm (1989) (10)
Integer sequences with big gaps and the pointwise ergodic theorem (1999) (10)
On the Two Weight Hilbert Transform Inequality (2013) (10)
An Estimate of the Maximal Operators Associated with Generalized Lacunary Sets (2004) (10)
On the A_2 inequality for Calderon-Zygmund Operators (2011) (9)
The perfect local Tb Theorem and twisted Martingale transforms (2012) (9)
Averages along the Square Integers: $\ell^p$ improving and Sparse Inequalities (2019) (8)
The bilinear Hilbert transform is pointwise finite (1997) (8)
Improving Estimates for Discrete Polynomial Averages (2019) (8)
The Linear Bound in A_2 for Calder\'on-Zygmund Operators: A Survey (2010) (8)
Two Weight Inequalities for Riesz Transforms (2013) (7)
On logarithmic bounds of maximal sparse operators (2018) (7)
Two Weight Inequalities for Maximal Truncations of Dyadic Calderón-Zygmund Operators (2009) (7)
On almost sure noncentral limit theorems (1991) (7)
Commutators of Cauchy type integrals for domains in $\C^n$ with minimal smoothness (2018) (6)
On the Local Tb Theorem: A Direct Proof under the Duality Assumption (2012) (6)
On an inequality due to Bourgain (1997) (6)
The return time theorem fails on infinite measure-preserving systems (1997) (6)
The bilinear maximal functions map into for . (2000) (6)
Commutators of Cauchy-Szego type integrals for domains in C^n with minimal smoothness (2021) (5)
A POLYNOMIAL ROTH THEOREM FOR CORNERS IN FINITE FIELDS (2020) (5)
Sparse Bounds for Maximal Monomial Oscillatory Hilbert Transforms (2016) (5)
The Walsh model for $M_2^*$ Carleson (2007) (5)
On a Lipschitz Variant of the Kakeya Maximal Function (2006) (5)
AN AFFINE RESTRICTION ESTIMATE IN R (2006) (5)
Laws of the iterated logarithm for partial sum processes indexed by functions (1989) (5)
L ESTIMATES FOR MAXIMAL AVERAGES ALONG ONE-VARIABLE VECTOR FIELDS IN R (2008) (4)
Non-Homogeneous Local $T1$ Theorem: Dual Exponents (2013) (4)
Small Ball and Discrepancy Inequalities (2006) (4)
VARIATIONS ON THE THEME OF JOURN ´ E'S LEMMA (2005) (4)
Estimates of the Discrepancy Function in Exponential Orlicz Spaces (2013) (4)
SPACES BETWEEN H1 AND L1 (2008) (4)
An Ap-Ainfinito inequality for the Hilbert transform (2012) (3)
Sparse Bounds for Bochner–Riesz Multipliers (2017) (3)
C A ] 6 O ct 2 00 9 SHARP A 2 INEQUALITY FOR HAAR SHIFT OPERATORS (2009) (3)
Dichotomy Results for the L1 Norm of the Discrepancy Function (2013) (3)
A Weak Type Inequality for Maximal Monomial Oscillatory Hilbert Transforms (2016) (3)
Two weight inequalities for positive operators: doubling cubes (2018) (3)
An A_p --A_infty inequality for the Hilbert Transform (2011) (2)
On the Hilbert Transform and C^2 Families of Lines (1999) (2)
On convergence of oscillatory ergodic Hilbert transforms (2016) (2)
$\ell^p$-improving estimates for discrete polynomial averages via bounds for exponential sums (2019) (2)
Haar Shifts, Commutators, and Hankel Operators (2008) (2)
THE KATO SQUARE ROOT PROBLEM ON AN ARBITRARY DOMAIN OF R d (2020) (2)
Bourgain's Entropy Criteria (1996) (2)
Weak and Strong type $ A_p$ Estimates for Calder\'on-Zygmund Operators (2010) (2)
Commutators of Cauchy--Szeg\H{o} type integrals for domains in $\mathbb C^n$ with minimal smoothness. (2019) (2)
Weighted estimates for one-sided martingale transforms (2018) (2)
Wiener-Wintner for Hilbert Transform (2006) (2)
A characterization of the two weight norm inequality for the Hilbert transform (2010) (2)
Third Order Commutator and Product BMO (2003) (1)
Rubio de Francia Littlewood Paley Inequalities and Directional Maximal Functions (2004) (1)
Sharp Estimates of the Sobolev Norm ofuTimes the Gradient ofv (1997) (1)
Spectral criteria, SLLN's and A.S. convergence of series of stationary variables (1996) (1)
Notification of error: Multiparameter Riesz commutators (2021) (1)
Three Dimensional Corners: A Box Norm Proof (2008) (1)
Oscillatory Singular Integrals and Sparse Operators (2016) (1)
Borderline Variants of the Muckenhoupt-Wheeden Inequality for Maximal Singular Integrals (2015) (1)
On the Local $ Tb$ Theorem under Minimal Integrability (2012) (1)
Laws of the iterated logarithm for the empirical characteristic function (1989) (1)
The solution of Katos conjectures (2001) (1)
Weighted bounds for maximal Walsh-Fourier series (2011) (1)
Endpoint $\ell^r$ improving estimates for prime averages (2021) (1)
On the Discrepancy Function in Arbitary Dimension, Close to L ^{1} (2006) (1)
A MAXIMAL FUNCTION CHARACTERIZATION OF THE HARDY SPACE FOR THE GAUSS MEASURE (2013) (1)
Improving Estimates for Discrete Polynomial Averages (2020) (0)
Ju n 20 04 Carleson ’ s Theorem : Proof , Complements , Variations (2004) (0)
Multi-Parameter Nehari Theorems (2007) (0)
On the convergence of multiple ergodic means (2022) (0)
ON A COUNTEREXAMPLE RELATED TO WEIGHTED WEAK TYPE ESTIMATES FOR SINGULAR (2015) (0)
On a Stein Conjecture on the Hilbert Transform on Vector Fields (2007) (0)
Locating the maximum of some stationary guassian sequences (1988) (0)
PROCEEDINGS OF THE INTERNET ANALYSIS SEMINAR ON: RIESZ TRANSFORMS ASSOCIATED TO SCHRÖDINGER OPERATORS (2015) (0)
ON THE EXPECTED NUMBER OF ZEROS OF A RANDOM HARMONIC POLYNOMIAL (2008) (0)
Weak Type Bound for Oscillatory Singular Integrals (2016) (0)
Ju n 20 03 Issues related to Rubio de Francia ’ s Littlewood – Paley Inequailty : A Survey (2003) (0)
The vector valued quartile operator (2012) (0)
Local Tb theorem with L2 testing conditions and general measures: square functions (2017) (0)
Weak-type estimates for Haar shift operators: Sharp power on the A(p) characteristic (2009) (0)
Commutators in the two-weight setting (2016) (0)
On logarithmic bounds of maximal sparse operators (2019) (0)
Pointwise convergence of vector-valued Fourier series (2013) (0)
Dynamical systems, fractional Brownian motion and limit theorems (1989) (0)
ul 2 00 3 Carleson ’ s Theorem : Proof , Complements , Variations (2008) (0)
Sparse endpoint estimates for Bochner–Riesz multipliers on the plane (2018) (0)
Some Limit Theorems (Empirical Processes) (1987) (0)
An elementary proof of the A2 bound (2017) (0)
HEISENBERG PAIRS IN THE PLANE. THREE PARALLEL LINES (2013) (0)
Weak and strong type estimates for maximal truncations of Calderón-Zygmund operators on Ap weighted spaces (2012) (0)
On the Hilbert transform and lacunary directions in the plane (2000) (0)
Weak Convergence to Self-Affine Processes in Dynamical Systems (1993) (0)
Improving and maximal inequalities for primes in progressions (2021) (0)
How to Win a Fellowship for Graduate Study in Mathematics (2004) (0)
C A ] 1 0 M ay 2 01 7 ON CONVERGENCE OF OSCILLATORY ERGODIC HILBERT TRANSFORMS (2018) (0)
ay 2 00 1 Carleson ’ s Theorem with Quadratic Phase Functions (2008) (0)
THE ATOMIC DECOMPOSITION IN L(R) (2007) (0)
J an 2 00 2 A Weak – type Orthogonality Principle (2008) (0)
Konstantin Ilyich Oskolkov, Friend and Colleague (2012) (0)
Carleson's theorem with quadratic phase (2001) (0)
On the Hilbert Transform and $C^{1+\ze}$ Families of Lines (2003) (0)
On Convergence of Modulated Ergodic Hilbert Transforms (2016) (0)
C A ] 4 J an 2 01 6 COMMUTATORS IN THE TWO-WEIGHT SETTING (2021) (0)

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