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Publications Influence

Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations

- J. Bourgain
- Mathematics
- 1 March 1993

1,416 250

Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity

- J. Bourgain
- Mathematics
- 1998

442 71

Another look at Sobolev spaces

- J. Bourgain, H. Brezis, P. Mironescu
- Mathematics
- 2001

The standard seminorm in the space $W^{s,p}$, with $s$<$1$, does not converge, when $s$ approaches $1$, to the corresponding $W^{1,p}$ seminorm. We prove that continuity is restored provided we… Expand

368 65- PDF

Periodic nonlinear Schrödinger equation and invariant measures

- J. Bourgain
- Mathematics
- 1 December 1994

AbstractIn this paper we continue some investigations on the periodic NLSEiuu +iuxx +u|u|p-2 (p≦6) started in [LRS]. We prove that the equation is globally wellposed for a set of data Φ of full… Expand

273 64- PDF

On lipschitz embedding of finite metric spaces in Hilbert space

- J. Bourgain
- Mathematics
- 1 March 1985

It is shown that anyn point metric space is up to logn lipeomorphic to a subset of Hilbert space. We also exhibit an example of ann point metric space which cannot be embedded in Hilbert space with… Expand

662 57

Averages in the plane over convex curves and maximal operators

- J. Bourgain
- Mathematics
- 1 December 1986

218 52

A sum-product estimate in finite fields, and applications

- J. Bourgain, N. Katz, T. Tao
- Mathematics
- 29 January 2003

AbstractLet A be a subset of a finite field
$$ F := \mathbf{Z}/q\mathbf{Z} $$ for some
prime q. If
$$ |F|^{\delta} < |A| < |F|^{1-\delta} $$
for some δ > 0, then we prove the estimate
$$ |A + A| +… Expand

424 49- PDF

Green's Function Estimates for Lattice Schrödinger Operators and Applications.

- J. Bourgain
- Mathematics
- 1 November 2004

Acknowledgment v CHAPTER 1: Introduction 1 CHAPTER 2: Transfer Matrix and Lyapounov Exponent 11 CHAPTER 3: Herman's Subharmonicity Method 15 CHAPTER 4: Estimates on Subharmonic Functions 19 CHAPTER… Expand

337 49- PDF

Besicovitch type maximal operators and applications to fourier analysis

- J. Bourgain
- Mathematics
- 1 June 1991

236 49

Bounds on Oscillatory Integral Operators Based on Multilinear Estimates

- J. Bourgain, L. Guth
- Mathematics
- 16 December 2010

We apply the Bennett–Carbery–Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We get improved Lp estimates in the Stein… Expand

196 44- PDF