A Sharp Bilinear Cone Restriction Estimate
نویسندگان
چکیده
منابع مشابه
A sharp bilinear cone restriction estimate
The purpose of this paper is to prove an essentially sharp L2 Fourier restriction estimate for light cones, of the type which is called bilinear in the recent literature. Fix d ≥ 3, denote variables in Rd by (x, xd) with x ∈ Rd−1, and let Γ = {x : xd = |x| and 1 ≤ xd ≤ 2}. Let Γ1 and Γ2 be disjoint conical subsets, i.e. Γi = {x ∈ Γ : x xd ∈ Ωi} where Ωi are disjoint closed subsets of the sphere...
متن کاملA Sharp Bilinear Restriction Estimate for Paraboloids
X iv :m at h/ 02 10 08 4v 2 [ m at h. C A ] 1 3 D ec 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon ...
متن کاملA Sharp Bilinear Restriction Estimate for Elliptic Surfaces
X iv :m at h/ 02 10 08 4v 1 [ m at h. C A ] 7 O ct 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon th...
متن کاملEndpoint Bilinear Restriction Theorems for the Cone, and Some Sharp Null Form Estimates
for some integer k. In both cases we call 2 the frequency of the waves φ, ψ. Red and blue waves both solve the free wave equation, but propagate along different sets of characteristics. Note that blue waves are the time reversal of red waves. Also, these waves are automatically smooth thanks to the frequency localization. The vector valued formulation will be convenient for technical reasons. W...
متن کاملA Sharp Bilinear Estimate for the Klein–gordon Equation in R
We prove a sharp bilinear estimate for the one dimensional Klein– Gordon equation. The proof involves an unlikely combination of five trigonometric identities. We also prove new estimates for the restriction of the Fourier transform to the hyperbola, where the pullback measure is not assumed to be compactly supported.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 2001
ISSN: 0003-486X
DOI: 10.2307/2661365