Related papers: Some sharp restriction inequalities on the sphere

In dimensions $d \in \{3,4,5,6,7\}$, we prove that the constant functions on the unit sphere $\mathbb{S}^{d-1}\subset \mathbb{R}^d$ maximize the weighted adjoint Fourier restriction inequality $$ \left| \int_{\mathbb{R}^d}…

The adjoint Fourier restriction inequality for the sphere $S^2$ states that if $f\in\lt(S^2,\sigma)$ then $\widehat{f\sigma}\in L^4(\reals^3)$. We prove that all critical points $f$ of the functional…

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…

Let $d\geq 2$ be an integer and let $2d/(d-1) < q \leq \infty$. In this paper we investigate the sharp form of the mixed norm Fourier extension inequality \begin{equation*} \big\|\widehat{f\sigma}\big\|_{L^q_{{\rm rad}}L^2_{{\rm…

We prove new Fourier restriction estimates to the unit sphere $S^{d-1}$ on the class of $O(d-k)\times O(k)$-symmetric functions, for every $d\geq 4$ and $2\leq k\leq d-2$. As an application, we establish the existence of maximizers for the…

In this article, we develop a linear profile decomposition for the $L^p \to L^q$ adjoint Fourier restriction operator associated to the sphere, valid for exponent pairs $p<q$ for which this operator is bounded. Such theorems are new when $p…

We prove that in dimensions $d \geq 3$, the non-endpoint, Lorentz-invariant $L^2 \to L^p$ adjoint Fourier restriction inequality on the $d$-dimensional hyperboloid $\mathbb{H}^d \subseteq \mathbb{R}^{d+1}$ possesses maximizers. The…

We prove the existence of functions that extremize the endpoint $L^2$ to $L^4$ adjoint Fourier restriction inequality on the one-sheeted hyperboloid in Euclidean space $\mathbb{R}^4$ and that, taking symmetries into consideration, any…

We prove weighted versions of the 2D Restriction Conjecture for the unit sphere in $\mathbb{R}^2$. Our results involve the weight functions $(1+|x|)^\alpha(1+|y|)^\beta$ and $(1+|x|+|y|)^\gamma$ with $\alpha,\beta,\gamma\geq 0$.

The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several…

We prove sharp $L^2$ Fourier restriction inequalities for compact, smooth surfaces in $\mathbb{R}^3$ equipped with the affine surface measure or a power thereof. The results are valid for all smooth surfaces and the bounds are uniform for…

We prove that constant functions are the unique real-valued maximizers for all $L^2-L^{2n}$ adjoint Fourier restriction inequalities on the unit sphere $\mathbb{S}^{d-1}\subset\mathbb{R}^d$, $d\in\{3,4,5,6,7\}$, where $n\geq 3$ is an…

We establish a sharp adjoint Fourier restriction inequality for the end-point Tomas-Stein restriction theorem on the circle under a certain arithmetic constraint on the support set of the Fourier coefficients of the given function. Such…

The Tomas-Stein inequality or the adjoint Fourier restriction inequality for the sphere $S^1$ states that the mapping $f\mapsto \hat{f\sigma}$ is bounded from $L^2(S^1)$ to $L^6(\mathbb{R}^2)$. We prove that there exists an extremizer for…

We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with colinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing…

We prove a new family of sharp $L^2(\mathbb S^{d-1})\to L^4(\mathbb R^d)$ Fourier extension inequalities from the unit sphere $\mathbb S^{d-1}\subset \mathbb R^d$, valid in arbitrary dimensions $d\geq 3$.

In this paper we prove a sharp trilinear inequality which is motivated by a program to obtain the sharp form of the $L^2 - L^6$ Tomas-Stein adjoint restriction inequality on the circle. Our method uses intricate estimates for integrals of…

This paper is devoted to establish a class of sharp Sobolev inequalities on the unit complex sphere as follows: 1) Case $0<d<Q=2n+2$: for any $f\in C^\infty$ and $2\leq q \leq \frac{2Q}{Q-d}$, \begin{equation*} \|f\|_q^2\leq…

The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping $f\mapsto \widehat{f\sigma}$ is bounded from $\lt(S^2)$ to $L^4(\reals^3)$. We prove that there exist functions which extremize this inequality, and that…

In this paper we obtain some sharp Hardy inequalities with weight functions that may admit singularities on the unit sphere. In order to prove the main results of the paper we use some recent sharp inequalities for the lowest eigenvalue of…