Alexander Barron

activity

20172020

most citedOn Global-in-Time Strichartz Estimates for the Semiperiodic Schrödinger Equation

20 citations · 54 across the 7 of their papers we have counts for

collaborators

8 papers

math.CA2020★ 3 cited

An $L^{4}$ maximal estimate for quadratic Weyl sums

Alex Barron

We show that $0 < t < 1 sup n = 1 \sum N e^{2 π i (n (\cdot) + n^{2} t)}_{L^{4} ([0, 1])} \leq C_{ε} N^{3/4 + ε}$ and discuss some applications to the theory…

math.AP2020

Global endpoint Strichartz estimates for Schrödinger equations on the cylinder $R \times T$

Alex Barron, Michael Christ, Benoit Pausader

We prove a sharp, global-in-time Strichartz estimate for the Schrödinger equation on the cylinder $R \times T$ .

math.CA2020★ 2 cited

Fourier decay of fractal measures on hyperboloids

Alex Barron, M. Burak Erdogan, Terence L. J. Harris

Let $μ$ be an $α$ -dimensional probability measure. We prove new upper and lower bounds on the decay rate of hyperbolic averages of the Fourier transform $μ$ . More precisely…

math.CA2020★ 3 cited

Restriction estimates for hyperboloids in higher dimensions via bilinear estimates

Alex Barron

Let $H$ be a $(d - 1)$ -dimensonal hyperbolic paraboloid in $R^{d}$ and let $E f$ be the Fourier extension operator associated to $H,$ with $f$ supported in $B…

math.AP2019★ 20 cited

On Global-in-Time Strichartz Estimates for the Semiperiodic Schrödinger Equation

Alexander Barron

We prove global-in-time Strichartz-type estimates for the Schrödinger equation on manifolds of the form $R^{n} \times T^{d}$ , where $T^{d}$ is a $d$ -dimen…

math.CA2018

Sparse domination and the strong maximal function

Alex Barron, Jose M. Conde-Alonso, Yumeng Ou +1

We study the problem of dominating the dyadic strong maximal function by $(1, 1)$ -type sparse forms based on rectangles with sides parallel to the axes, and show that such dominati…