collaborators
Showing math.CAShow all

3 papers · 1 filter

math.CA2025

The Kakeya Conjecture: where does it come from and why is it important?

Jonathan Hickman

Roughly speaking, the Kakeya Conjecture asks to what extent lines which point in different directions can be packed together in a small space. In , the problem is relatively…

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.CA2024

Spherical maximal estimates via geometry

Jonathan Hickman, Ajša Jančar

We present a simple geometric approach to studying the boundedness properties of Stein's spherical maximal operator, which does not rely on the Fourier transform. Using this,…