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Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
- J. Bourgain
- Mathematics
- 1 March 1993
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…
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…
Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity
- J. Bourgain
- Mathematics
- 1998
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…
Pointwise ergodic theorems for arithmetic sets
- J. Bourgain
- Mathematics
- 1 December 1989
converge almost surely for N -+ co, assuming f a function of class L~(~, ~). Here and in the sequel, one denotcs by ~ a probability measure and by T a measure-preserving automorphism. The natural…
Averages in the plane over convex curves and maximal operators
- J. Bourgain
- Mathematics
- 1 December 1986
A sum-product estimate in finite fields, and applications
- J. Bourgain, N. Katz, T. Tao
- Mathematics, Computer Science
- 29 January 2003
TLDR
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…
Besicovitch type maximal operators and applications to fourier analysis
- J. Bourgain
- Mathematics
- 1 June 1991
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