J. Hickman

activity

20152022

most citedNew Kakeya estimates using the polynomial Wolff axioms

2 citations · 6 across the 6 of their papers we have counts for

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math.AP2019★ 1 cited

Uniform $L^{p}$ Resolvent Estimates on the Torus

Jonathan Hickman

A new range of uniform $L^{p}$ resolvent estimates is obtained in the setting of the flat torus, improving previous results of Bourgain, Shao, Sogge and Yao. The arguments rely on th…

math.AP2019

On a higher dimensional version of the Benjamin--Ono equation

Felipe Linares, Oscar G. Riaño, Keith M. Rogers +2

We consider a higher dimensional version of the Benjamin--Ono equation, $\partial_{t} u - R_{1} Δ u + u \partial_{x_{1}} u = 0$ , where $R_{1}$ denotes the Riesz transform with…

math.AP2018

Sharp local smoothing estimates for Fourier integral operators

David Beltran, Jonathan Hickman, Christopher D. Sogge

The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe so…

Uniform Lp Resolvent Estimates on the Torus

On a higher dimensional version of the Benjamin--Ono equation

Sharp local smoothing estimates for Fourier integral operators

Uniform $L^{p}$ Resolvent Estimates on the Torus