João P. G. Ramos

activity

20172023

most citedRegularity of fractional maximal functions through Fourier multipliers

22 citations · 49 across the 17 of their papers we have counts for

collaborators

24 papers

math.CA2023

Sharp Gaussian decay for the one-dimensional harmonic oscillator

Danylo Radchenko, João P. G. Ramos

We prove a conjecture by Vemuri by proving sharp bounds on $ℓ^{κ}$ sums of Hermite functions multiplied by an exponentially decaying factor. More explicitly, we prove that, for ea…

math.AP2023

A Faber-Krahn type inequality for log-subharmonic functions in the hyperbolic ball

David Kalaj, João P. G. Ramos

Assume that $Δ_{h}$ is the hyperbolic Laplacian in the unit ball $B$ and assume that $Φ_{n}$ is the unique radial solution of Poisson equation $Δ_{h} lo g Φ_{n} = - 4 (n - 1)^{2}$ satis…

math.CA2022★ 2 cited

The Multilinear Spherical Maximal Function in one dimension

Georgios Dosidis, João P. G. Ramos

In dimension $n = 1$ we obtain $L^{p_{1}} (R) \times \dots \times L^{p_{m}} (R)$ to $L^{p} (R)$ boundedness for the multilinear spherical maximal function in the largest…

math.CA2022

On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles

Aleksei Kulikov, Lucas Oliveira, João P. G. Ramos

We make progress on a question by Vemuri on the optimal Gaussian decay of harmonic oscillators, proving the original conjecture up to an arithmetic progression of times. The techni…

math.FA2022

A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions

Károly J. Böröczky, Alessio Figalli, João P. G. Ramos

We prove that if a triplet of functions satisfies almost equality in the Prékopa-Leindler inequality, then these functions are close to a common log-concave function, up to multipl…

math.AP2022

Uniqueness of solutions to nonlinear Schrödinger equations from their zeros

Christoph Kehle, João P. G. Ramos

We show novel types of uniqueness and rigidity results for Schrödinger equations in either the nonlinear case or in the presence of a complex-valued potential. As our main result w…

math.CA2021★ 7 cited

Perturbed Fourier uniqueness and interpolation results in higher dimensions

João P. G. Ramos, Martin Stoller

We obtain new Fourier interpolation and -uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa, and by the second author. We show tha…

math.CA2020

Uniform bounds for oscillatory and polynomial Carleson operators

João P. G. Ramos

We prove that a variety of oscillatory and polynomial Carleson operators are uniformly bounded on the family of parameters under considerations. As a particular application of our…

math.CA2020

A note on discrete Heisenberg uniqueness pairs for the parabola

Felipe Gonçalves, João P. G. Ramos

We discuss on Heisenberg uniqueness pairs for the parabola given by discrete sequences along straight lines. Our method consists in linking the problem at hand with recent uniquene…

math.NT2020

Bounds for the Lonely Runner Problem via Linear Programming

Felipe Gonçalves, João P. G. Ramos

In this note we develop a linear programming framework to produce upper and lower bounds for the lonely runner problem.

math.AP2020

Maximal function estimates and local well-posedness for the generalized Zakharov--Kuznetsov equation

Felipe Linares, João P. G. Ramos

We prove a high-dimensional version of the Strichartz estimates for the unitary group associated to the free Zakharov--Kuznetsov equation. As a by--product, we deduce maximal estim…

math.AP2020

The Cauchy problem for the $L^{2} -$ critical generalized Zakharov-Kuznetsov equation in dimension 3

Felipe Linares, João P. G. Ramos

We prove local well-posedness for the $L^{2}$ critical generalized Zakharov-Kuznetsov equation in $H^{s}, s \in (3/4, 1) .$ We also prove that the equation is "almost well-posedness"…

math.CA2020★ 6 cited

Perturbed interpolation formulae and applications

João P. G. Ramos, Mateus Sousa

We employ functional analysis techniques in order to deduce that some classical and recent interpolation results in Fourier analysis can be suitably perturbed. As an application of…

math.CA2020★ 4 cited

New Sign Uncertainty Principles

Felipe Gonçalves, Diogo Oliveira e Silva, João P. G. Ramos

We prove new sign uncertainty principles which vastly generalize the recent developments of Bourgain, Clozel & Kahane and Cohn & Gonçalves, and apply our results to a variety of sp…

math.CA2020

On regularity and mass concentration phenomena for the sign uncertainty principle

Felipe Gonçalves, Diogo Oliveira e Silva, João P. G. Ramos

The sign uncertainty principle of Bourgain, Clozel & Kahane asserts that if a function $f : R^{d} \to R$ and its Fourier transform $f$ are nonpositive at the…

math.CA2020

On optimal autocorrelation inequalities on the real line

José Madrid, João P. G. Ramos

We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work. In particular, we obtain improvements on the sharp constants in some of the inequalities p…

math.CA2020

On the endpoint behaviour of oscillatory maximal function

Tainara Borges, Cynthia Bortolotto, João P. G. Ramos

Inspired by a question of Lie, we study boundedness in subspaces of $L^{1} (R)$ of oscillatory maximal functions. In particular, we construct functions in $L^{1} (R)$ w…

math.CA2019

Fourier uniqueness pairs of powers of integers

João P. G. Ramos, Mateus Sousa

We prove, under certain conditions on $(α, β)$ , that each Schwartz function $f$ such that $f (\pm n^{α}) = f^(\pm n^{β}) = 0, \forall n \geq 0$ must vanish identically, complementing…

math.CA2019★ 8 cited

Weak differentiability for fractional maximal functions of general $L^{p}$ functions on domains

João P. G. Ramos, Olli Saari, Julian Weigt

Let $Ω \subset R^{n}$ be bounded a domain. We prove under certain structural assumptions that the fractional maximal operator relative to $Ω$ maps $L^{p} (Ω) \to W^{1, p} (Ω)$ …

math.CA2019

The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals

João P. G. Ramos

We make progress on an interesting problem on the boundedness of maximal modulations of the Hilbert transform along the parabola. Namely, if we consider the multiplier arising from…

math.CA2019

Low-dimensional maximal restriction principles for the Fourier transform

João Pedro Ramos

Following the ideas from a paper by the same author, we prove abstract maximal restriction results for the Fourier transform. Our results deal mainly with maximal operators of conv…

math.CA2018

Maximal restriction estimates and the maximal function of the Fourier transform

João P. G. Ramos

We prove a maximal restriction inequality for the Fourier transform, providing an answer to a question left open by Müller, Ricci and Wright. Our methods are similar to the ones in…

math.CA2018★ 22 cited

Regularity of fractional maximal functions through Fourier multipliers

David Beltran, João Pedro Ramos, Olli Saari

We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$ . We also show that…

math.CA2017

Sharp total variation results for maximal functions

João Pedro Ramos

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 Pérez Lá…

Sharp Gaussian decay for the one-dimensional harmonic oscillator

A Faber-Krahn type inequality for log-subharmonic functions in the hyperbolic ball

The Multilinear Spherical Maximal Function in one dimension

On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles

A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions

Uniqueness of solutions to nonlinear Schrödinger equations from their zeros

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Uniform bounds for oscillatory and polynomial Carleson operators

A note on discrete Heisenberg uniqueness pairs for the parabola

Bounds for the Lonely Runner Problem via Linear Programming

Maximal function estimates and local well-posedness for the generalized Zakharov--Kuznetsov equation

The Cauchy problem for the L2−critical generalized Zakharov-Kuznetsov equation in dimension 3

Perturbed interpolation formulae and applications

New Sign Uncertainty Principles

On regularity and mass concentration phenomena for the sign uncertainty principle

On optimal autocorrelation inequalities on the real line

On the endpoint behaviour of oscillatory maximal function

Fourier uniqueness pairs of powers of integers

Weak differentiability for fractional maximal functions of general Lp functions on domains

The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals

Low-dimensional maximal restriction principles for the Fourier transform

Maximal restriction estimates and the maximal function of the Fourier transform

Regularity of fractional maximal functions through Fourier multipliers

Sharp total variation results for maximal functions

The Cauchy problem for the $L^{2} -$ critical generalized Zakharov-Kuznetsov equation in dimension 3

Weak differentiability for fractional maximal functions of general $L^{p}$ functions on domains