2 citations · 6 across the 9 of their papers we have counts for
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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…
Uniform Resolvent Estimates on the Torus
Jonathan Hickman
A new range of uniform 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…
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…
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, , where denotes the Riesz transform with…