相关论文: A sharp bilinear restriction estimate for parabolo…
We prove $L^p$ estimates for the shifted bilinear Hilbert transform, with a polylogarithmic bound in the size of the shift. As applications, we obtain $r$-variation estimates for bilinear ergodic averages in the sharp range $r > 2$, a sharp…
The goal of this paper is to prove bilinear $L^p$ estimates for rough dispersive evolutions satisfying non-degeneracy and transversality assumptions. The estimates generalize the sharp Fourier extension estimates for the cone and the…
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…
This is a continuation of the paper "Restriction theorem for Fourier-Dunkl transform I: Cone surface, J. Pseudo-Differ. Oper. Appl. 14(1), Paper No. 5 (2023)", where the authors introduced and studied the Fourier-Dunkl transform on…
We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in threedimensional euclidean space. Our approach exploits in a crucial way the…
We prove bilinear $\ell^2$-decoupling and refined bilinear decoupling inequalities for the truncated hyperbolic paraboloid in $\mathbb{R}^3$. As an application, we prove the associated restriction estimate in the range $p>22/7$, matching an…
We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from…
In this article, we prove a bilinear estimate for Schr\"odinger equations on 2d waveguide, $\mathbb{R}\times \mathbb{T}$. We hope it may be of use in the further study of concentration compactness for cubic NLS on $\mathbb{R}\times…
We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.
We continue our research on Fourier restriction for hyperbolic surfaces, by studying local perturbations of the hyperbolic paraboloid $z=xy$ which are of the form $z=xy+h(y),$ where $h(y)$ is a smooth function which is flat at the origin.…
A new decomposition for frequency-localized solutions to the Schrodinger equation is given which describes the evolution of the wavefunction using a weighted sum of Lipschitz tubes. As an application of this decomposition, we provide a new…
In this short note, we prove that the restriction conjecture for the (hyperbolic) paraboloid in $\mathbb{R}^d$ implies the $l^p$-decoupling theorem for the (hyperbolic) paraboloid in $\mathbb{R}^{2d-1}$. In particular, this gives a simple…
We prove generalized Fefferman-Stein type theorems on sharp functions with $A_p$ weights in spaces of homogeneous type with either finite or infinite underlying measure. We then apply these results to establish mixed-norm weighted…
We first review the $L^2$ bilinear generalizations of the $L^4$ estimate of Strichartz for solutions of the homogeneous 3D wave equation, and give a short proof based solely on an estimate for the volume of intersection of two thickened…
We derive sparse bounds for the bilinear spherical maximal function in any dimension $d\geq 1$. When $d\geq 2$, this immediately recovers the sharp $L^p\times L^q\to L^r$ bound of the operator and implies quantitative weighted norm…
In this paper, we prove the restriction estimates for 2D surfaces S:= {(xi1, xi2, xi1^3 +/- xi2^3) : (xi1, xi2) in [0,1]^2} by reducing to Wang-Wu's result on the perturbed paraboloid and to the results on the perturbed hyperboloid obtained…
The restriction conjecture is one of the famous problems in harmonic analysis. There have been many methods developed in the study of the conjecture for the paraboloid. In this paper, we generalize the multilinear method of Bourgain and…
We prove L^p estimates for a two-dimensional bilinear operator of paraproduct type. This result answers a question posed by Demeter and Thiele in [3].
In this paper we study the restriction estimate for the flat disk over finite fields. Mockenhaupt and Tao initially studied this problem but their results were addressed only for dimensions $n=4,6$. We improve and extend their results to…
We propose a new approach to the Fourier restriction conjectures. It is based on a discretization of the Fourier extension operators in terms of quadratically modulated wave packets. Using this new point of view, and by combining natural…