95 citations · 226 across the 23 of their papers we have counts for
29 papers
Estimates for variants of Gowers norms
Vjekoslav Kovač, Keith M. Rogers
Motivated by a log-convexity question of Bennett and Tao, we consider Gowers-type functionals defined by norms of multiple autocorrelations. We prove sharp bounds in terms of…
Orthonormal Sobolev estimates with fractal measures
Neal Bez, Keith M. Rogers, Shunya Toyoshima
We prove a fractal version of Lieb's Hardy-Littlewood-Sobolev inequality for orthonormal functions. On the one hand, this can be viewed as a trace theorem for orthonormal functions…
Reconstruction for the Calderón problem with Lipschitz conductivities
Pedro Caro, María Ángeles García-Ferrero, Keith M. Rogers
We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant a…
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…
Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane
Pedro Caro, Keith M. Rogers
For potentials and with compact support, we consider the Schrödinger equation $-(\nabla +iA)…
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…