Related papers: Sharp extension inequalities on finite fields

In this article, we prove that all global, nonendpoint Fourier restriction inequalities for the paraboloid in $\mathbb R^{1+d}$ have extremizers and that $L^p$-normalized extremizing sequences are precompact modulo symmetries. This result…

Among the class of functions on the circle with Fourier modes up to degree 120, constant functions are the unique real-valued maximizers for the endpoint Tomas-Stein inequality.

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…

We show that, for $n\geq 3$, $\lim_{t \to 0} e^{it\Delta}f(x) = f(x)$ holds almost everywhere for all $f \in H^s (\mathbb{R}^n)$ provided that $s>\frac{n}{2(n+1)}$. Due to a counterexample by Bourgain, up to the endpoint, this result is…

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…

We consider the adjoint restriction inequality associated to the hypersurface $\{(\tau, \xi) : \tau = \pm|\xi|^2, \;\xi \in \mathbb{R}^d\}$ at the Stein-Tomas exponent. Extremizers exist in all dimensions and extremizing sequences are…

We prove a sharp Fourier extension inequality on the circle for the Tomas-Stein exponent for functions whose spectrum $\{\pm \lambda_n\}$ satisfies $\lambda_{n+1}>3 \lambda_{n}$.

We study sharp $p$-variational inequalities for the Hardy-Littlewood maximal operator on complete graphs, answering in the affirmative a question by Feng Liu and Qingying Xue. We also use computational assistance to find sharp constants in…

We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain-Katz-Tao finite field incidence theorem derived from sum-product estimates. In…

In this paper, we will use a suitable tranform to investigate the sharp constants and optimizers for the following Caffarelli-Kohn-Nirenberg inequalities for a wide range of parameters $(r,p,q,s,\mu,\sigma)$ and $0\leq a\leq1$:…

For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction…

In this article, we prove some total variation inequalities for maximal functions. Our results deal with two possible generalizations of the results contained in Aldaz and P\'erez L\'azaro's work, one of whose considers a variable…

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…

We study the quantitative stability associated with the adjoint Fourier restriction inequality, focusing on the paraboloid and two-dimensional sphere cases. We show that these Strichartz-stability inequalities admit minimizers attaining…

We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p<2$, while it…

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.

In this article, we study the problem of obtaining Lebesgue space inequalities for the Fourier restriction operator associated to rectangular pieces of the paraboloid and perturbations thereof. We state a conjecture for the dependence of…

In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…

We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants uniform in the…

Given a smooth curve with nonzero curvature $\Sigma\subset \mathbb{R}^2$, let $E_{\Sigma}$ denote the associated Fourier extension operator. For both general compact curves and the parabola, we characterize the pairs $(p,q)\in [1,\infty]^2$…