Dominique Maldague

activity

20182025

most citedImproved decoupling for the parabola

7 citations · 20 across the 17 of their papers we have counts for

collaborators

17 papers

math.CO2025

Heilbronn's triangle problem in three dimensions

Dominique Maldague, Hong Wang, Dmitrii Zakharov

We show that among any $n$ points in the unit cube one can find a triangle of area at most $n^{- 2/3 - c}$ for some absolute constant $c > 0$ . This gives the first non-trivial upper bo…

math.CA2025

Sharp local smoothing estimates for curve averages

Shengwen Gan, Dominique Maldague, Changkeun Oh

We prove sharp local smoothing estimates for curve averages in all dimensions. As a corollary, we prove the sharp $L^{p}$ boundedness of the helical maximal operator in $\mathbb{R}^4…

math.CA2025

Tangency counting for well-spaced circles

Dominique Maldague, Alexander Ortiz

In the late 90's, Tom Wolff introduced the circle tangency counting problem in his expository article on the Kakeya conjecture. For collections of well-spaced circles, we break the…

math.CA2024

On the small cap decoupling for the moment curve in $R^{3}$

Dominique Maldague, Changkeun Oh

This paper proves sharp small cap decoupling estimates for the moment curve $M^{n} = {(t, t^{2}, \dots, t^{n}) : 0 \leq t \leq 1}$ in the remaining small cap parameter ranges for $\m…

cs.DS2023

Estimating the matrix $p \to q$ norm

Larry Guth, Dominique Maldague, John Urschel

The matrix $p \to q$ norm is a fundamental quantity appearing in a variety of areas of mathematics. This quantity is known to be efficiently computable in only a few specia…

math.CA2023

A sharp square function estimate for the moment curve in $R^{n}$

Larry Guth, Dominique Maldague

We use high-low frequency methods developed in the context of decoupling to prove sharp (up to $C_{ε} R^{ε}$ ) square function estimates for the moment curve $(t, t^{2}, \dots, t^{n})$ in $\ma…

math.CA2023★ 1 cited

Small cap decoupling for the paraboloid in $R^{n}$

Larry Guth, Dominique Maldague, Changkeun Oh

We extend the small cap decoupling program established by Demeter, Guth, and Want to paraboloids in $R^{n}$ for some range of $p$ .

math.CA2022

A sharp square function estimate for the moment curve in $R^{3}$

Dominique Maldague

We prove a sharp (up to $C_{ε} R^{ε}$ ) $L^{7}$ square function estimate for the moment curve in $R^{3}$ .

math.CA2022★ 2 cited

An exceptional set estimate for restricted projections to lines in $R^{3}$

Shengwen Gan, Larry Guth, Dominique Maldague

Let $γ : [0, 1] \to S^{2}$ be a non-degenerate curve in $R^{3}$ , that is to say, $det (γ (θ), γ^{'} (θ), γ^{''} (θ)) \neq = 0$ . For each $θ \in [0, 1]$ , let $l_θ=\{tγ(θ)…

math.CA2022★ 2 cited

Small cap decoupling for the moment curve in $R^{3}$

Larry Guth, Dominique Maldague

We prove sharp small cap decoupling estimates for the moment curve in $R^{3}$ . Our formulation of the small caps is motivated by a conjecture about $L^{p}$ estimates for expon…

math.CA2022★ 3 cited

On restricted projections to planes in $R^{3}$

Shengwen Gan, Shaoming Guo, Larry Guth +3

Let $γ : [0, 1] \to S^{2}$ be a non-degenerate curve in $R^{3}$ , that is to say, $det (γ (θ), γ^{'} (θ), γ " (θ)) \neq = 0$ . For each $θ \in [0, 1]$ , let $V_θ=γ(θ)^\pe…

math.CA2022

Amplitude dependent wave envelope estimates for the cone in $R^{3}$

Dominique Maldague, Larry Guth

For functions $f$ with Fourier transform supported in the truncated cone, we bound superlevel sets ${x \in R^{3} : ∣ f (x) ∣ > α}$ using an $α$ -dependent version of the wave envelo…

math.CA2021★ 1 cited

Sharp superlevel set estimates for small cap decouplings of the parabola

Yuqiu Fu, Larry Guth, Dominique Maldague

We prove sharp bounds for the size of superlevel sets ${x \in R^{2} : ∣ f (x) ∣ > α}$ where $α > 0$ and $f : R^{2} \to C$ is a Schwartz function with Fourier transform s…

math.CA2021★ 4 cited

Decoupling inequalities for short generalized Dirichlet sequences

Yuqiu Fu, Larry Guth, Dominique Maldague

We study decoupling theory for functions on $R$ with Fourier transform supported in a neighborhood of short Dirichlet sequences ${lo g n}_{n = N + 1}^{N + N^{1/2}}$ , as well a…

math.CA2020★ 7 cited

Improved decoupling for the parabola

Larry Guth, Dominique Maldague, Hong Wang

We prove an $(l^{2}, l^{6})$ decoupling inequality for the parabola with constant $(lo g R)^{c}$ . In the appendix, we present an application to the six-order correlation of the integer s…

math.CA2019

Special cases of power decay in multilinear oscillatory integrals

Dong Dong, Dominique Maldague, Dominick Villano

We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered by existing theory. Considerati…

math.CA2018

A constrained optimization problem for the Fourier transform: Quantitative analysis

Dominique Maldague

Among functions $f$ majorized by indicator functions $1_{E}$ , which functions have maximal ratio $∥ f ∥_{q} /∣ E ∣^{1/ p}$ ? We establish a quantitative answer to this question fo…

Heilbronn's triangle problem in three dimensions

Sharp local smoothing estimates for curve averages

Tangency counting for well-spaced circles

On the small cap decoupling for the moment curve in R3

Estimating the matrix p→q norm

A sharp square function estimate for the moment curve in Rn

Small cap decoupling for the paraboloid in Rn

A sharp square function estimate for the moment curve in R3

An exceptional set estimate for restricted projections to lines in R3

Small cap decoupling for the moment curve in R3

On restricted projections to planes in R3

Amplitude dependent wave envelope estimates for the cone in R3

Sharp superlevel set estimates for small cap decouplings of the parabola

Decoupling inequalities for short generalized Dirichlet sequences

Improved decoupling for the parabola

Special cases of power decay in multilinear oscillatory integrals

A constrained optimization problem for the Fourier transform: Quantitative analysis

On the small cap decoupling for the moment curve in $R^{3}$

Estimating the matrix $p \to q$ norm

A sharp square function estimate for the moment curve in $R^{n}$

Small cap decoupling for the paraboloid in $R^{n}$

A sharp square function estimate for the moment curve in $R^{3}$

An exceptional set estimate for restricted projections to lines in $R^{3}$

Small cap decoupling for the moment curve in $R^{3}$

On restricted projections to planes in $R^{3}$

Amplitude dependent wave envelope estimates for the cone in $R^{3}$