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Recent progress on the Restriction conjecture (2003)
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by Terence Tao
Citations:
40 - 5 self
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Citations
509
Endpoints Strichartz estimates
- Keel, Tao - 1998
491
Harmonic Analysis
- Stein - 1993
339
Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
- Strichartz - 1977
273
Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
- Kenig, Ponce, et al. - 1993
207
A bilinear estimate with applications to the KdV equation
- Kenig, Ponce, et al. - 1996
175
Refinements of Strichartz’ inequality and applications to 2D-NLS with critical nonlinearity
- Bourgain - 1998
160
On convergence and growth of partial sums of Fourier series
- Carleson - 1966
147
Space-time estimates for null forms and the local existence theorem
- Klainerman, Machedon - 1993
138
Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds
- Burq, Gérard, et al.
103
Recent work connected with the Kakeya problem, Prospects in mathematics
- Wolff - 1996
98
Inequalities for strongly singular convolution operators
- Fefferman - 1970
93
A restriction theorem for the Fourier transform
- Tomas - 1975
81
Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace (d’après Bourgain
- Ginibre - 1995
78
Strichartz estimates for a Schrödinger operator with nonsmooth coefficients
- Staffilani, Tataru
75
An improved bound for Kakeya type maximal functions
- Wolff - 1995
74
Fourier integrals in classical analysis”, Cambridge Tracts in Mathematics 105,
- Sogge - 1993
74
Decay of circular means of Fourier transforms of measures, Internat
- Wolff - 1999
73
A sharp bilinear restriction estimates for paraboloids
- Tao
67
Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients II,
- Tataru - 2001
66
A bilinear approach to the restriction and Kakeya conjectures
- Tao, Vargas, et al. - 1998
65
A sharp bilinear cone restriction estimate
- Wolff
64
Oscillatory Integrals and a Multiplier Problem for the Disc
- Carleson, Sjolin
62
The multiplier problem for the ball,
- Fefferman - 1971
59
Multilinear weighted convolution of L 2 functions, and applications to non-linear dispersive equations
- Tao
58
Regularity properties of Fourier integral operators
- Seeger, Sogge, et al. - 1991
53
The Kakeya maximal function and the spherical summation multipliers
- Córdoba - 1977
53
On Fourier coefficients and transforms of functions of two variables, Stud
- Zygmund - 1974
50
Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
- Bourgain - 1993
46
On the dimension of Kakeya sets and related maximal inequalities, Geom
- Bourgain - 1999
44
A bilinear approach to cone multipliers
- Tao, Vargas
41
A note on spherical summation multipliers
- Fefferman - 1973
41
Rough solutions of the Einstein-vacuum equations
- Klainerman, Rodnianski - 2005
40
From rotating needles to stability of waves: emerging connections between combinatorics, analysis
- Tao
39
On limits of sequences of operators,
- Stein - 1961
33
Some analytic problems to related to statistical mechanics. - In: Euclidean Harmonic Analysis,
- Carleson - 1979
31
Besicovitch-type maximal operators and applications to Fourier analysis, GAFA 22
- Bourgain - 1991
31
The Bochner-Riesz conjecture implies the Restriction conjecture
- Tao
30
On Kakeya’s problem and a similar one
- Besicovitch - 1928
29
A remark on Schrodinger operators. -
- Bourgain - 1992
29
Restriction theorems and maximal operators related to oscillatory integrals
- Moyua, Vargas, et al. - 1999
28
Sharp local well-posedness results for the nonlinear wave equation
- Smith, Tataru - 2005
26
Endpoint bilinear restriction theorem for the cone, and some sharp null form estimates
- Tao - 2001
24
Estimates for cone multipliers, Operator Theory
- Bourgain - 1995
22
Improved bounds for Bochner–Riesz and maximal Bochner–Riesz operators
- Lee
21
Harmonic analysis and combinatorics: How much may they contribute to each other?, Mathematics: Frontiers and perspectives, IMU/Amer
- Bourgain
21
Some problems in harmonic analysis, in: “Harmonic analysis in Euclidean spaces
- Stein - 1978
20
Some new estimates on oscillatory integrals, Essays in Fourier Analysis in honor of
- Bourgain - 1995
20
sets and restriction properties of Fourier transforms
- Mockenhaupt, Salem
19
Weighted estimates for the Helmholtz equation and some applications
- Barceló, Ruiz, et al. - 1997
19
Homogeneous L 2 Bilinear estimates for wave equations
- Foschi, Klainerman
19
Bounds in Lebesgue Spaces of Oscillatory Integral Operators
- Mockenhaupt - 1996
18
Summation of multiple Fourier series by spherical means
- Bochner - 1936
18
A note on the cone multiplier
- Mockenhaupt - 1993
17
A note of the restriction of the Fourier transform to spheres
- Beckner, Carbery, et al. - 1989
16
On the restriction of the Fourier transform to a conical surface
- Barcelo - 1985
16
On almost everywhere convergence of Bochner–Riesz means in higher dimensions
- Christ - 1985
16
Tao: Recent progress on the Kakeya conjecture
- Katz, T
16
Wave front sets, local smoothing and Bourgain’s circular maximal theorem
- Mockenhaupt, Seeger, et al. - 1992
16
A generalization of Bourgain’s circular maximal theorem
- Schlag - 1997
15
Restriction implies Bochner-Riesz for paraboloids
- Carbery - 1992
15
Propagation of singularities and maximal functions in the plane
- Sogge - 1991
12
Dispersive estimates and the 2D cubic NLS equation
- Planchon
11
Maximal functions, covering lemmas and Fourier multipliers, in Harmonic analysis in Euclidean spaces (Proc
- Córdoba - 1978
10
Averages over curves with torsion
- Oberlin, Smith, et al. - 1998
10
Restriction theorems for the Fourier transform to some manifolds in R n,
- Prestini - 1979
9
The boundedness of the maximal Bochner-Riesz operator on
- Carbery - 1983
8
Weighted inequalities for Bochner–Riesz means in the plane
- Carbery, Seeger
8
Some sharp restriction theorems for homogeneous manifolds,
- Carli, Iosevich - 1998
8
Weak-type endpoint bounds for Riesz means
- Tao - 1996
8
The weak-type endpoint Bochner-Riesz conjecture and related topics
- Tao - 1998
7
On the restriction and multiplier problem
- Bourgain - 1991
7
A physical space approach to wave equation bilinear estimates
- Klainerman, Rodnianski, et al.
6
A note on the Kakeya maximal operator
- Barrionuevo - 1996
6
Restriction of the Fourier transform to submanifolds of low codimension
- Christ - 1982
6
Roth’s theorem in the primes, preprint
- Green
6
Local smoothing estimates related to the circular maximal theorem
- Schlag, Sogge - 1997
5
Geometric Fourier analysis, Ann
- Córdoba - 1982
5
Kakeya and restriction phenomena for finite fields
- Mockenhaupt, Tao
5
Edinburgh lecture notes on the Kakeya problem, available at http://www.math.ucla.edu/∼tao/preprints
- Tao
4
Lectures on Bochner-Riesz means
- Davis, Chang - 1987
4
A restriction theorem for the Fourier transform
- Mockenhaupt
4
A geometric proof of the circular maximal theorem
- Schlag - 1998
4
Some remarks on restriction of the Fourier transform for general measures
- Sjlin, Soria - 1999
4
Non-endpoint bilinear cone restriction theorems, unpublished. 61
- Tao
4
Maximal averages and packing of one-dimensional sets
- Wolff
4
Local smoothing estimates in L p for large p
- Wolff
3
estimates for the Bochner–Riesz operator of negative order
- Bak, Sharp - 1997
3
Negative results for Nikodym maximal functions and related oscillatory integrals in curved space
- Sogge - 1997
3
On the maximal Bochner-Riesz conjecture in the plane for p < 2
- Tao
2
Restriction of the Fourier transform to quadratic submanifolds
- Banner - 2002
2
A local smoothing estimate in higher dimensions, preprint
- ̷Laba, Wolff
2
On the summability almost everywhere of the multiple Fourier series at the critical index
- Sunouchi - 1985
1
A bilinear extension inequality in two dimensions, preprint
- Barcelo, Bennett, et al.
1
Shadi Tahvidar-Zadeh, Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential, preprint
- Burq, Planchon, et al.
1
On the Bochner-Riesz means of critical order
- Liflyand - 1997
1
Time decay for solutions of Schroedinger equations with rough and time-dependent potentials, preprint
- Rodnianski, Schlag
1
Weak-type estimates for maximal operators on certain H p spaces
- Stein, Taibleson, et al. - 1981