A Fourier restriction theorem for a two-dimensional surface of finite type

Stefan Buschenhenke, Detlef Müller, Ana Vargas

Type: Article

Publication Date: 2017-05-09

Citations: 22

DOI: https://doi.org/10.2140/apde.2017.10.817

Abstract

The problem of $L^p(R^3)\to L^2(S)$ Fourier restriction estimates for smooth hypersurfaces S of finite type in R^3 is by now very well understood for a large class of hypersurfaces, including all analytic ones. In this article, we take up the study of more general $L^p(R^3)\to L^q(S)$ Fourier restriction estimates, by studying a prototypical class of two-dimensional surfaces with strongly varying curvature conditions. Our approach is based on an adaptation of the so-called bilinear method. We discuss several new features arising in the study of this problem.

Locations

Analysis & PDE - View
arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	$L^p-L^2$ Fourier restriction for hypersurfaces in $\Bbb R^3$: Part I	2012	Isroil A. Ikomov Detlef Müller
+	$L^p-L^2$ Fourier restriction for hypersurfaces in $\Bbb R^3$: Part I	2012	Isroil A. Ikomov Detlef Müller
+	$L^p-L^2$ Fourier restriction for hypersurfaces in $\Bbb R^3$: Part II	2014	Isroil A. Ikromov Detlef Müller
+	A uniform Fourier restriction theorem for surfaces in ℝ³	2003	Daniel M. Oberlin
+	Fourier restriction estimates for surfaces of co-dimension two in $\mathbb{R}^5$	2020	Shaoming Guo Changkeun Oh
+	$L^2$ affine Fourier restriction theorems for smooth surfaces in $\mathbb{R}^3$	2022	Jianhui Li
+	A restriction estimate using polynomial partitioning	2015	Lawrence Guth
+	A restriction estimate using polynomial partitioning	2014	Larry Guth
+	A restriction estimate using polynomial partitioning	2014	Larry Guth
+	A Fourier restriction theorem for a perturbed hyperboloid	2018	Stefan Buschenhenke Detlef Müller Ana Vargas
+	Fourier restriction estimates for surfaces of co-dimension two in ℝ5	2022	Shaoming Guo Changkeun Oh
+ PDF Chat	Book Review: Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra	2018	Andreas Seeger
+	Fourier restriction for smooth hyperbolic 2-surfaces	2020	Stefan Buschenhenke Detlef Müller Ana Vargas
+	A restriction estimate for polynomial surfaces with negative Gaussian curvatures	2020	Shaoming Guo Changkeun Oh
+	A Fourier restriction theorem for a perturbed hyperbolic paraboloid	2018	Stefan Buschenhenke Detlef Müller Ana Vargas
+ PDF Chat	Fourier restriction for smooth hyperbolic 2-surfaces	2022	Stefan Buschenhenke Detlef Müller Ana Vargas
+	A Fourier restriction theorem for a perturbed hyperbolic paraboloid	2018	Stefan Buschenhenke Detlef Müller Ana Vargas
+	Some remarks on Fourier restriction estimates	2017	Jongchon Kim
+	A restriction estimate for surfaces with negative Gaussian curvatures	2020	Shaoming Guo Changkeun Oh
+	A restricted $2$-plane transform related to Fourier Restriction for surfaces of codimension $2$	2022	Spyridon Dendrinos Andrei Mustaţǎ Marco Vitturi

Works That Cite This (21)

Action	Title	Year	Authors
+	On Fourier restriction for finite-type perturbations of the hyperboloid	2019	Stefan Buschenhenke Detlef Müller Ana Vargas
+ PDF Chat	Sharp $$L^p$$ estimates for oscillatory integral operators of arbitrary signature	2022	Jonathan Hickman Marina Iliopoulou
+	The Almost Optimal Multilinear Restriction Estimate for Hypersurfaces with Curvature: The Case of<i>n-1</i>Hypersurfaces in ℝn	2021	Ioan Bejenaru
+ PDF Chat	Partitions of Flat One-Variate Functions and a Fourier Restriction Theorem for Related Perturbations of the Hyperbolic Paraboloid	2021	Stefan Buschenhenke Detlef Müller Ana Vargas
+ PDF Chat	Fourier restriction above rectangles	2021	Jeremy Schwend Betsy Stovall
+ PDF Chat	A Restriction Estimate for a Certain Surface of Finite Type in $${\mathbb {R}}^3$$	2021	Zhuoran Li Changxing Miao Jiqiang Zheng
+ PDF Chat	A Fourier restriction theorem for a perturbed hyperbolic paraboloid	2019	Stefan Buschenhenke Detlef Müller Ana Vargas
+	Restriction inequalities for the hyperbolic hyperboloid	2020	Benjamin Baker Bruce Diogo Oliveira e Silva Betsy Stovall
+ PDF Chat	Transference of bilinear restriction estimates to quadratic variation norms and the Dirac–Klein–Gordon system	2018	Timothy Candy Sebastian Herr
+ PDF Chat	A Fourier restriction theorem for a perturbed hyperbolic paraboloid: polynomial partitioning	2022	Stefan Buschenhenke Detlef Müller Ana Vargas

Works Cited by This (40)

Action	Title	Year	Authors
+ PDF Chat	Some Recent Progress on the Restriction Conjecture	2004	Terence Tao
+	Endpoint estimates for the circular maximal function	2002	Sanghyuk Lee
+	Estimates for Cone Multipliers	1995	Jean Bourgain
+	Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals	2002	Elias M. Stein Timothy S Murphy
+	Bilinear restriction estimates for surfaces with curvatures of different signs	2005	Sanghyuk Lee
+	From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE	2000	Terence Tao
+	A sharp $$L^p-L^q$$ L p - L q -Fourier restriction theorem for a conical surface of finite type	2015	Stefan Buschenhenke
+	A bilinear approach to cone multipliers I. Restriction estimates	2000	Terence Tao Ana Vargas
+	Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations	1977	Robert S. Strichartz
+	A sharp bilinear restriction estimate for paraboloids	2002	Terence Tao