R. Quilodrán

activity

20092019

most citedNonexistence of extremals for the adjoint restriction inequality on the hyperboloid

33 citations · 84 across the 5 of their papers we have counts for

collaborators

5 papers

math.CA2019

Smoothness of solutions of a convolution equation of restricted-type on the sphere

Diogo Oliveira e Silva, René Quilodrán

Let $S^{d - 1}$ denote the unit sphere in Euclidean space $R^{d}$ , $d \geq 2$ , equipped with surface measure $σ_{d - 1}$ . An instance of our main result concerns the reg…

math.CA2018★ 4 cited

A comparison principle for convolution measures with applications

Diogo Oliveira e Silva, René Quilodrán

We establish the general form of a geometric comparison principle for $n$ -fold convolutions of certain singular measures in $R^{d}$ which holds for arbitrary $n$ and $d$ . Th…

math.CA2011★ 33 cited

Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

René Quilodrán

We study the problem of existence of extremizers for the $L^{2}$ to $L^{p}$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an…

math.CA2011★ 30 cited

On extremizing sequences for the adjoint restriction inequality on the cone

René Quilodrán

It is known that extremizers for the $L^{2}$ to $L^{6}$ adjoint Fourier restriction inequality on the cone in $R^{3}$ exist. Here we show that nonnegative extremizing sequences…

math.CO2009★ 17 cited

The joints problem in R^n

René Quilodrán

We show that given a collection of A lines in \R^n, n\geq 2, the maximum number of their joints (points incident to at least n lines whose directions form a linearly independent se…