arXiv subjects

Diogo Oliveira e Silva

Publications and source records attributed to Diogo Oliveira e Silva.

41 records · Page 3Linked to original sources

arXiv2015

A sharp trilinear inequality related to Fourier restriction on the circle

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 sixfold products of Bessel functions developed in a companion paper. We also establish that constants are local extremizers of the Tomas-Stein adjoint restriction inequality as well as of another inequality appearing in the program.

math.CA↗

arXiv2014

Some sharp restriction inequalities on the sphere

In this paper we find the sharp forms and characterize the complex-valued extremizers of the adjoint Fourier restriction inequalities on the sphere $$\big\|\widehat{f σ}\big\|_{L^{p}(\mathbb{R}^{d})} \lesssim \|f\|_{L^{q}(\mathbb{S}^{d-1},σ)}$$ in the cases $(d,p,q) = (d,2k, q)$ with $d,k \in \mathbb{N}$ and $q\in \mathbb{R}^+ \cup \{\infty\}$ satisfying: (a) $k = 2$, $q \geq 2$ and $3 \leq d\leq 7$; (b) $k = 2$, $q \geq 4$ and $d \geq 8$; (c) $k \geq 3$, $q \geq 2k$ and $d \geq 2$. We also prove a sharp multilinear weighted restriction inequality, with weight related to the $k$-fold convolution of the surface measure.

math.CA↗

arXiv2012

Extremizers for Fourier restriction inequalities: convex arcs

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 sequence of nonnegative functions has a subsequence which converges to an extremizer.

math.CA↗

arXiv2012

Nonexistence of extremizers for certain convex curves

We establish the nonexistence of extremizers for a local Fourier restriction inequality on a certain class of planar convex curves whose curvature satisfies a natural assumption. We accomplish this by studying the local behavior of the triple convolution of the arclength measure on the curve with itself, and show in particular that every extremizing sequence concentrates at a point on the curve.

math.CA↗

arXiv2011

On Trilinear Oscillatory Integrals

We examine a certain class of trilinear integral operators which incorporate oscillatory factors e^{iP}, where P is a real-valued polynomial, and prove smallness of such integrals in the presence of rapid oscillations.

math.CA↗