2 citations · 6 across the 6 of their papers we have counts for
9 papers · 1 filter
A non-archimedean variant of Littlewood--Paley theory for curves
Jonathan Hickman, James Wright
We prove a variant of a square function estimate for the extension operator associated to the moment curve in non-archimedean local fields. The arguments rely on a structural analy…
Sobolev improving for averages over curves in
David Beltran, Shaoming Guo, Jonathan Hickman +1
We study -Sobolev improving for averaging operators given by convolution with a compactly supported smooth density on a non-degenerate curve. In particular, in 4 d…
Sharp estimates for oscillatory integral operators of arbitrary signature
Jonathan Hickman, Marina Iliopoulou
The sharp range of -estimates for the class of Hörmander-type oscillatory integral operators is established in all dimensions under a general signature assumption on the phase…
The circular maximal operator on Heisenberg radial functions
David Beltran, Shaoming Guo, Jonathan Hickman +1
Lebesgue space estimates are obtained for the circular maximal function on the Heisenberg group restricted to a class of Heisenberg radial functions. Under this assu…
Improved bounds for the Kakeya maximal conjecture in higher dimensions
Jonathan Hickman, Keith M. Rogers, Ruixiang Zhang
We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to the context of the Kakeya problem. By writing out the induction argument as a recursive algo…
New Kakeya estimates using the polynomial Wolff axioms
Jonathan Hickman, Keith M Rogers
We obtain new bounds for the Kakeya maximal conjecture in most dimensions , as well as improved bounds for the Kakeya set conjecture when or . For this we consider…