Related papers: Bilinear Fourier restriction theorems

This dissertation studies the Fourier restriction, which is to find the range of the constants p, q such that the L^q norm on a chosen subset of the Fourier domain is bounded above by the L^p norm in a spacial domain, up to some constant…

Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we…

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…

We prove uniform $L^p \to L^q$ bounds for Fourier restriction to polynomial curves in $\mathbb R^d$ with affine arclength measure, in the conjectured range.

Bilinear restriction estimates have been appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the…

An $L^2$ Fourier restriction argument of Bak and Seeger is abstracted to the setting of locally compact abelian groups. This is used to prove new restriction estimates for varieties lying in modules over local fields or rings of integers…

Let $P$ denote the $3$-dimensional paraboloid over a finite field of odd characteristic in which $-1$ is not a square. We show that the Fourier extension operator associated with $P$ maps $L^2$ to $L^{r}$ for $r > \frac{32}{9} \approx…

We prove $L^p \rightarrow L^q$ Fourier restriction estimates for 3-dimensional quadratic surfaces in $\mathbb{R}^5$. Our results are sharp, up to endpoints, for a few classes of surfaces.

We prove global Fourier restriction estimates for elliptic, or two-sheeted, hyperboloids of arbitrary dimension $d \geq 2$, extending recent joint work with Oliveira e Silva and Stovall. Our results are unconditional in the (adjoint)…

We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…

A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $L^p-L^q$ restriction…

We study bilinear $L^2$ Fourier restriction estimates which are related to the 2d wave equation in the sense that we restrict to subsets of thickened null cones. In an earlier paper we studied the corresponding 3d problem, obtaining several…

In connection with the restriction problem in $\mathbb R^n$ for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates…

We prove an $L^2 \times L^2 \rightarrow L_t^qL_x^p $ bilinear Fourier extension estimate for the cone when $p,q$ are on the critical line $1/q=(\frac{n+1}{2})(1-1/p)$. This extends previous results by Wolff, Tao and Lee-Vargas.

We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two…

We use the polynomial partitioning method of Guth to prove weighted Fourier restriction estimates in $\Bbb R^3$ with exponents $p$ that range between $3$ and $3.25$, depending on the weight. As a corollary to our main theorem, we obtain new…

Recently Wolff obtained a sharp $L^2$ 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 and spheres.…

We present a restriction theorem for the Fourier transform to a 2-dimensional conical surface of finite type, obtaining a sharp result, which improves previous work by Barcelo.

The goal of this paper is to provide a new approach to address the $L^p-$boundedness of bilinear rough singular integral operators. This approach relies on local Fourier series expansion of input functions leading to trilinear estimates…

In this work, we study Fourier multipliers on noncommutative spaces. In particluar, we show a simple proof of $L^p$-$L^q$ estimate of Fourier multipliers on general noncommutative spaces associated with semi-finite von Neumann algebras.…