scholarly journals A sharp bilinear restriction estimate for paraboloids

2003 ◽  
Vol 13 (6) ◽  
pp. 1359-1384 ◽  
Author(s):  
Terence Tao
Keyword(s):  
Restriction Estimate

scholarly journals Improved restriction estimate for hyperbolic surfaces inR3

2017 ◽  
Vol 273 (3) ◽  
pp. 917-945 ◽  
Author(s):  
Chu-Hee Cho ◽  
Jungjin Lee
Keyword(s):  
Hyperbolic Surfaces ◽  
Restriction Estimate

A Restriction Theorem for a k-Surface in ℝn

2005 ◽  
Vol 48 (2) ◽  
pp. 260-266 ◽  
Author(s):  
Daniel M. Oberlin
Keyword(s):  
Restriction Theorem ◽  
Fourier Restriction ◽  
Restriction Estimate

AbstractWe establish a sharp Fourier restriction estimate for a measure on a k-surface in ℝn, where n = k(k + 3)/2.

Reduction to Restriction Estimates near the Principal Root Jet

2016 ◽  
Author(s):  
Isroil A. Ikromov ◽  
Detlef Müller
Keyword(s):  
Newton Polyhedron ◽  
Small Letter ◽  
Fourier Restriction ◽  
Restriction Estimate

This chapter shows that one may reduce the desired Fourier restriction estimate to a piece Ssubscript Greek small letter psi of the surface S lying above a small, “horn-shaped” neighborhood Dsubscript Greek small letter psi of the principal root jet ψ‎, on which ∣x₂ − ψ‎(x₁)∣ ≤ ε‎xᵐ₁. Here, ε‎ > 0 can be chosen as small as one wishes. The proof then provides the opportunity to introduce some of the basic tools which will be applied frequently, such as dyadic domain decompositions, rescaling arguments based on the dilations associated to a given edge of the Newton polyhedron, in combination with Greenleaf's restriction and Littlewood–Paley theory, hence summing the estimates that have been obtained for the dyadic pieces.

scholarly journals Slicing surfaces and the Fourier restriction conjecture

2009 ◽  
Vol 52 (2) ◽  
pp. 515-527 ◽  
Author(s):  
Fabio Nicola
Keyword(s):  
Fourier Transform ◽  
Finite Type ◽  
Fourier Restriction ◽  
The Fourier Transform ◽  
Restriction Estimate

AbstractWe deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid and the elliptic hyperboloid in ℝn implies that for the cone in ℝn+1. We also prove a new restriction estimate for any surface in ℝ3 locally isometric to the plane and of finite type.

Sign in / Sign up

Export Citation Format

Share Document