42 citations · 118 across the 19 of their papers we have counts for
24 papers
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…
Lacunary maximal functions on homogeneous groups
Aswin Govindan Sheri, Jonathan Hickman, James Wright
We observe that classical arguments of Ricci--Stein can be used to prove bounds for maximal functions associated to lacunary dilates of a fixed measure in the setting of homo…
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…
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…
Sharp bounds for the helical maximal function
David Beltran, Shaoming Guo, Jonathan Hickman +1
We establish the boundedness of the helical maximal function for the sharp range . Our results improve the previous known bounds for . The key ingredi…
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…