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Another look at Sobolev spaces
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
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
On lipschitz embedding of finite metric spaces in Hilbert space
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
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
A sum-product estimate in finite fields, and applications
A Szemerédi-Trotter type theorem in finite fields is proved, and a new estimate for the Erdös distance problem in finite field, as well as the three-dimensional Kakeya problem in infinite fields is obtained.
Bounds on Oscillatory Integral Operators Based on Multilinear Estimates
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