Related papers: $L^p-L^2$ Fourier restriction for hypersurfaces in…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

If $S$ is a smooth compact surface in $\mathbb{R}^3$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3.25$, $\| E_S f\|_{L^p(\mathbb{R}^3)} \le C(p,S) \| f…

In this paper we introduce a new type of restriction problem, called the \textit{restriction problem with moments}. We show that the surface area measure of the sphere satisfies the $L^p$-$L^2$ restriction problem with moments if $1 \leq p…

In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem…

This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions…

In this paper we prove several results on the geometry of surfaces immersed in $\mathbf R^3$ with small or bounded $L^2$ norm of $|A|$. For instance, we prove that if the $L^2$ norm of $|A|$ and the $L^p$ norm of $H$, $p>2$, are…

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 explore the connection between $k$-broad Fourier restriction estimates and sharp regularity $L^p-L^q$ local smoothing estimates for the solutions of the wave equation in $\mathbb{R}^{n}\times \mathbb{R}$ for all $n \geq 3$ via a…

Recently, L. Guth improved the restriction estimate for the surfaces with strictly positive Gaussian curvature in R3. In this paper we generalize his restriction estimate to the surfaces with strictly negative Gaussian curvature.

We prove an $l^p$ decoupling inequality for hypersurfaces with nonzero Gaussian curvature and use it to derive a corresponding $l^p$ decoupling for curves not contained in a hyperplane. This extends our earlier work from [2]

This is the continuation of our paper [10]. In this paper which is self contained, we would like to give a different obstruction formula to the FIRST order deformation of the pair of a smooth curve and a smooth hypersurface. This…

In this note we show that the strong spherical maximal function in $\mathbb R^d$ is bounded on $L^p$ if $p>2(d+1)/(d-1)$ for $d\ge 3$.

We consider certain Littlewood-Paley square functions on $\Bbb R^2$ and prove sharp estimates for them, from which we can deduce $L^p$ boundedness of maximal functions defined by Fourier multipliers of Bochner-Riesz type on $\Bbb R^2$. This…

The $L^p$ convergence of eigenfunction expansions for the Laplacian on planar domains is largely unknown for $p\neq 2$. After discussing the classical Fourier series on the 2-torus, we move onto the disc, whose eigenfunctions are explicitly…

In this paper we study the linear series $|L-3p|$ of hyperplane sections with a triple point $p$ on a surface $S$ embedded via a very ample line bundle $L$ for a \emph{general} point $p$. If this linear series does not have the expected…

In terms of the Fourier-Haar coefficients, a criterion is obtained for the function $f (x_1,x_2)$ to belong to the net space $N_{\bar{p},\bar{q}}(M)$ and to the Lebesgue space $L_{\bar{p}}[0,1]^2$ with mixed metric, where…

We give various conditions for Hermite pseudo-multipliers to be bounded on $L^2(\mathbb{R}^n)$. As a by-product we also give results on $L^p(\mathbb{R}^n)$, as well as new results for pseudo-multipliers for the Gaussian measure setting. One…

We apply geometric incidence estimates in positive characteristic to prove the optimal $L^2 \to L^3$ Fourier extension estimate for the paraboloid in the four-dimensional vector space over a prime residue field. In three dimensions, when…

We give a simple proof of the sharp decay of the Fourier-transform of surface-carried measures of two-dimensional generic surfaces. The estimates are applied to prove Strichartz and resolvent estimates for elliptic operators whose…

Let M be a compact manifold of dimension n, P = P(h) a semiclassical pseudodifferential operator on M, and u = u(h) an L^2 normalised family of functions such that Pu is O(h) in L^2(M) as h goes to 0. Let H be a compact submanifold of M. In…