3 papers
math.CA2025
Improved bounds for the strong spherical maximal operator
Jonathan Hickman, Joshua Zahl
We study the mapping properties of the strong spherical maximal function, which is a multiparameter generalisation of Stein's spherical maximal function. We show that this op…
math.CA2023
Off-diagonal estimates for the helical maximal function
David Beltran, Jennifer Duncan, Jonathan Hickman
The optimal mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analys…
math.CA2023
Pointwise convergence for the Schrödinger equation [After Xiumin Du and Ruixiang Zhang]
Jonathan Hickman
This expository essay accompanied the author's presentation at the Séminaire Bourbaki on 01 April 2023. It describes the breakthrough work of Du--Zhang on the Carleson problem for…