#21,120

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American mathematician

F. Michael Christmathematics Degrees

Mathematics

#897

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#1581

Historical Rank

Measure Theory

#783

World Rank

#1039

Historical Rank

Mathematics

- PhD Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley

According to Wikipedia, Francis Michael Christ is an American mathematician and professor at University of California, Berkeley, specializing in harmonic analysis, partial differential equations, and several complex variables. He is known for the Christ–Kiselev maximal inequality.

- A T(b) theorem with remarks on analytic capacity and the Cauchy integral (1990) (793)
- The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals (2005) (249)
- Lectures on singular integral operators (1991) (236)
- Weak Type (1, 1) Bounds for Rough Operators (1988) (230)
- Ill-posedness for nonlinear Schrodinger and wave equations (2003) (215)
- Polynomial growth estimates for multilinear singular integral operators (1987) (186)
- Singular and maximal Radon transforms: analysis and geometry (1999) (156)
- Best constants for two nonconvolution inequalities (1995) (155)
- Multidimensional van der Corput and sublevel set estimates (1999) (149)
- On the restriction of the Fourier transform to curves: endpoint results and the degenerate case (1985) (131)
- Ü BOUNDS FOR SPECTRAL MULTIPLIERS ON NILPOTENT GROUPS (2009) (131)
- bounds for spectral multipliers on nilpotent groups (1991) (125)
- Hilbert transforms along curves I. Nilpotent groups (1985) (119)
- Global ^{∞} irregularity of the ∂-Neumann problem for worm domains (1996) (118)
- Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities (2005) (110)
- Convolution, curvature, and combinatorics: a case study (1998) (96)
- Weak type (1, 1) bounds for rough operators, II (1988) (93)
- Nilpotent Group C*-algebras as Compact Quantum Metric Spaces (2002) (85)
- Maximal operators related to the Radon transform and the Calderon-Zygmund method of rotations (1986) (82)
- Existence of Extremals for a Fourier Restriction Inequality (2010) (77)
- POWER SERIES SOLUTION OF A NONLINEAR SCHR ¨ ODINGER EQUATION (2005) (73)
- Weak (1,1) bounds for oscillatory singular integrals (1987) (72)
- Pseudodifferential operators on groups with dilations (1992) (72)
- A priori bounds and weak solutions for the nonlinear Schr (2006) (68)
- Regularity Properties of the ∂ b Equation on Weakly Pseudoconvex CR Manifolds of Dimension 3 (1988) (65)
- Singular integral characterizations of Hardy spaces on homogeneous groups (1984) (64)
- Operators associated to flat plane curves: $L^p$ estimates via dilation methods (1989) (64)
- On multilinear oscillatory integrals, nonsingular and singular (2003) (63)
- Communication lower bounds and optimal algorithms for programs that reference arrays - Part 1 (2013) (62)
- On the extremizers of an adjoint Fourier restriction inequality (2010) (55)
- On the $$\bar \partial $$ equation in weightedL2 norms in ℂ1equation in weightedL2 norms in ℂ1 (1991) (53)
- Counterexamples to analytic hypoellipticity for domains of finite type (1992) (53)
- OnLp spectral multipliers for a solvable lie group (1996) (52)
- Certain sums of Squares of Vector Fields Fail to be Analytic Hypoelliptic (1991) (50)
- Hypoellipticity in the infinitely degenerate regime (2001) (46)
- A sharpened Hausdorff-Young inequality (2014) (45)
- $L^p $ estimates for maximal functions and Hilbert transforms along flat convex curves in ${\mathbf{R}}^2 $ (1986) (39)
- Regularity properties of the \overline∂_{} equation on weakly pseudoconvex CR manifolds of dimension 3 (1988) (38)
- A note on weighted norm inequalities for the Hardy-Littlewood maximal operator (1983) (36)
- Instability of the periodic nonlinear Schrodinger equation (2003) (36)
- Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids (2010) (36)
- Weak Type Endpoint Bounds for Bochner-Riesz Multipliers (1987) (35)
- The extension problem for certain function spaces involving fractional orders of differentiability (1984) (35)
- Near-extremizers of Young's Inequality for R^d (2011) (34)
- Near Equality in the Brunn-Minkowski Inequality (2012) (33)
- A remark on singular Calderón-Zygmund theory (1987) (31)
- Intermediate optimal gevrey exponents occur (1996) (30)
- QUASIEXTREMALS FOR A RADON-LIKE TRANSFORM (2011) (30)
- Inversion in Some Algebras of Singular Integral Operators (1988) (30)
- Vector ₂ weights and a Hardy-Littlewood maximal function (2001) (29)
- Necessary conditions for vector‐valued operator inequalities in harmonic analysis (2005) (29)
- The Szegö projection need not preserve global analyticity (1996) (28)
- A Necessary Condition For Analytic Hypoellipticity (1994) (28)
- Extremizers of a Radon transform inequality (2011) (27)
- The strong maximal function on a nilpotent group (1992) (26)
- A sharpened Riesz-Sobolev inequality (2017) (24)
- Analytic hypoellipticity breaks down for weakly pseudoconvex Reinhardt domains (1991) (24)
- Nonuniqueness of weak solutions of the nonlinear Schroedinger equation (2005) (23)
- Near equality in the two-dimensional Brunn-Minkowski inequality (2012) (23)
- Mixed norm estimates for a restricted X-ray transform (2002) (23)
- HYPOELLIPTICITY OF THE KOHN LAPLACIAN FOR THREE-DIMENSIONAL TUBULAR CAUCHY–RIEMANN STRUCTURES (2002) (22)
- On the regularity of inverses of singular integral operators (1988) (22)
- An Approximate Inverse Riesz-Sobolev Inequality (2011) (21)
- Hilbert transforms along curves, II: A flat case (1985) (21)
- Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type (2003) (20)
- ON CERTAIN ELEMENTARY TRILINEAR OPERATORS (2001) (19)
- Hypoellipticity: Geometrization and speculation (1998) (19)
- Some non-analytic-hypoelliptic sums of squares of vector fields (1992) (19)
- On extremals for a Radon-like transform (2011) (18)
- A Convolution Inequality Concerning Cantor-Lebesgue Measures. (1985) (17)
- Analytic hypoellipticity, representations of nilpotent groups, and a nonlinear eigenvalue problem (1993) (17)
- Upper bounds for Bergman kernels associated to positive line bundles with smooth Hermitian metrics (2013) (17)
- On Trilinear Oscillatory Integrals (2011) (16)
- Near Equality in the Riesz-Sobolev Inequality (2013) (15)
- Global analytic hypoellipticity in the presence of symmetry (1994) (14)
- Sharp Hardy-Littlewood-Sobolev Inequalities on Quaternionic Heisenberg Groups (2014) (14)
- Remarks on Global Irregularity in the @{Neumann Problem (1999) (14)
- Near-extremizers of Young's inequality for discrete groups (2011) (14)
- Bounds For Multilinear Sublevel Sets Via Szemeredi's Theorem (2011) (13)
- Weighted norm inequalities and Schur's Lemma (1984) (13)
- L(p) Estimates for Maximal Functions and Hilbert-Transforms Along Flat Convex Curves in R(2) (2013) (13)
- Embedding compact three-dimensional CR manifolds of finite type in $\mathbf{C}^n$ (1989) (13)
- LP ESTIMATES FOR MAXIMAL FUNCTIONS AND HILBERT TRANSFORMS ALONG FLAT CONVEX CURVES IN R (2007) (13)
- Trilinear smoothing inequalities and a variant of the triangular Hilbert transform. (2020) (12)
- Sharp Hardy–Littlewood–Sobolev inequalities on the octonionic Heisenberg group (2014) (11)
- LEBESGUE SPACE BOUNDS FOR ONE-DIMENSIONAL GENERALIZED RADON TRANSFORMS (2008) (11)
- On random multilinear operator inequalities (2011) (11)
- On Holder-Brascamp-Lieb inequalities for torsion-free discrete Abelian groups (2015) (11)
- A remark on sums of squares of complex vector fields (2005) (11)
- Examples of analytic non-hypoellipticity of ∂b (1994) (10)
- A class of hypoelliptic PDE admitting nonanalytic solutions (1992) (10)
- Off-diagonal decay of Bergman kernels: On a conjecture of Zelditch (2013) (10)
- A weak type (1,1) inequality for maximal averages over certain sparse sequences (2011) (10)
- Cases of equality in certain multilinear inequalities of Hardy-Riesz-Brascamp-Lieb-Luttinger type (2013) (10)
- Inequalities of Riesz-Sobolev type for compact connected abelian groups (2018) (10)
- On Trilinear Oscillatory Integral Inequalities and Related Topics (2020) (10)
- Multilinear Oscillatory Integrals Via Reduction of Dimension (2011) (10)
- Remarks on the Breakdown of Analyticity for ∂ b and Szegö Kernels (1991) (9)
- Examples of singular maximal functions unbounded on Lp (1991) (9)
- Smoothness of extremizers of a convolution inequality (2010) (8)
- Near-extremizers of Young’s inequality for Euclidean groups (2019) (8)
- Examples pertaining to Gevrey hypoellipticity (1997) (8)
- LOCAL SOLVABILITY FOR A CLASS OF PARTIAL DIFFERENTIAL OPERATORS WITH DOUBLE CHARACTERISTICS (1995) (8)
- Mixed norm estimates for certain generalized Radon transforms (2005) (8)
- Pointwise estimates for the relative fundamental solution of ∂b (1988) (8)
- 6. Nonexistence of Invariant Analytic Hypoelliptic Differential Operators on Nilpotent Groups of Step Greater than Two (1995) (7)
- Endpoint Lebesgue estimates for weighted averages on polynomial curves (2017) (7)
- Analytic hypoellipticity in dimension two (1996) (7)
- Analytic Capacity and the Cauchy Integral (1991) (7)
- Infinite dimensional families of locally nonsolvable partial differential operators (1995) (6)
- Pointwise estimates for the relative fundamental solution of \overline∂_{} (1988) (6)
- On Young's inequality for Heisenberg groups (2017) (5)
- Maximizers of Rogers-Brascamp-Lieb-Luttinger functionals in higher dimensions (2017) (5)
- The optimal constants in Holder-Brascamp-Lieb inequalities for discrete Abelian groups (2013) (5)
- Subsets of Euclidean Space with Nearly Maximal Gowers Norms (2015) (5)
- On local and global analytic and Gevrey hypoellipticity (1995) (5)
- A three term sublevel set inequality (2022) (5)
- Near equality in the Riesz-Sobolev inequality in higher dimensions (2015) (5)
- HARDY-LITTLEWOOD MAXIMAL OPERATOR (2016) (5)
- On an extremization problem concerning Fourier coefficients (2015) (4)
- On the equation and Szegö projection on CR manifolds (1989) (4)
- Global endpoint Strichartz estimates for Schrödinger equations on the cylinder R×T (2021) (4)
- Equality in Brascamp-Lieb-Luttinger Inequalities (2017) (4)
- A class of singular bilinear maximal functions (2022) (4)
- Pointwise convergence of certain continuous-time double ergodic averages (2020) (4)
- SPIRALING AND NONHYPOELLIPTICITY FOR CR STRUCTURES DEGENERATE ALONG TRANSVERSE REAL CURVES (2000) (3)
- Estimates for fundamental solutions of second-order subelliptic differential operators (1989) (3)
- Chapter Five. Extremizers of a Radon Transform Inequality (2014) (3)
- Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation (2009) (3)
- On the $L^1$ behavior of eigenfunction expansions and singular integral operators (1987) (3)
- A triangular Hilbert transform with curvature (2020) (3)
- A family of degenerate differential operators (1993) (3)
- Off-Diagonal Decay of Bergman Kernels: On a Question of Zelditch (2013) (2)
- Global Irregularity for Mildly Degenerate Elliptic Operators (1995) (2)
- Characterization of $H^1$ by singular integrals: Necessary conditions (1984) (2)
- REMARKS ON ANALYTIC HYPOELLIPTICITY OF ∂̅b (1996) (2)
- Global $C^\nf$ Irregularity of the $\bar\partial$--Neumann Problem for Worm Domains (1995) (1)
- Examples of H\"older-stable Phase Retrieval (2022) (1)
- Spiraling and nonhypoellipticity (2001) (1)
- On implicitly oscillatory quadrilinear integrals (2022) (1)
- On Analytic Solvability and Hypoellipticity For $\dbar$ and $\dbar_b (1995) (1)
- On nearly radial product functions (2015) (1)
- Global endpoint Strichartz estimates for Schr\"odinger equations on the cylinder $\mathbb{R}\times\mathbb{T}$ (2020) (0)
- HYPOELLIPTICITY OF THE KOHN LAPLACIAN FOR THREE-DIMENSIONAL TUBULAR CR STRUCTURES (2005) (0)
- Temporal Regularity for Random Walk on Discrete Nilpotent Groups (2020) (0)
- BOUNDS FOR MULTILINEAR SUBLEVEL SETS (2008) (0)
- Modulation Invariant and Multilinear Singular Integral Operators [after Lacey and Thiele] (2006) (0)
- A symmetrization inequality shorn of symmetry (2018) (0)
- Sharp Hardy–Littlewood–Sobolev inequalities on the octonionic Heisenberg group (2016) (0)
- Modulation invariant and multilinear singular integral operators (2006) (0)
- IMPLICITLY OSCILLATORY MULTILINEAR INTEGRALS FIRST ENCOUNTERS WITH THE FIFTH KIND (2022) (0)
- On an apparently bilinear inequality for the Fourier transform (2015) (0)
- Near Equality in the Riesz-Sobolev Inequality (2019) (0)
- Inverses of Singular Integral Operators (1991) (0)
- Ü BOUNDS FOR SPECTRAL MULTIPLIERS ON NILPOTENT (2009) (0)
- On analytic solvability and hypoellipticity for $\overline{\partial }$ and $\overline{\partial }_b$ (1997) (0)
- On Young’s Convolution Inequality for Heisenberg Groups (2021) (0)
- Subsets of Euclidean Space with Nearly Maximal Gowers Norms (2019) (0)
- NONUNIQUENESS OF GENERALIZED SOLUTIONS OF THE NAVIER-STOKES EQUATION (2005) (0)
- Remarks on Global Irregularity in the d-bar-Neumann Problem (1999) (0)
- Global Irregularity For Degenerate Elliptic Operators (1995) (0)

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