26 citations · 51 across the 8 of their papers we have counts for
8 papers · 1 filter
estimates for the Hilbert transforms along a one-variable vector field
Michael Bateman, Christoph Thiele
Stein conjectured that the Hilbert transform in the direction of a vector field is bounded on, say, whenever is Lipschitz. We establish a wide range of estimates fo…
Single annulus estimates for Hilbert transforms along vector fields
Michael Bateman
We prove , estimates on the Hilbert transform along a one variable vector field acting on functions with frequency support in an annulus. Estimates when $p>2…
Maximal averages along a planar vector field depending on one variable
Michael Bateman
We prove (essentially) sharp estimates for a restricted maximal operator associated to a planar vector field that depends only on the horizontal variable. The proof combines…
New Bounds on cap sets
Michael Bateman, Nets Hawk Katz
We provide an improvement over Meshulam's bound on cap sets in . We show that there exist universal and so that any cap set in has size at most $C {3^N \…
An estimate from below for the Buffon needle probability of the four-corner Cantor set
Michael Bateman, Alexander Volberg
Let $\Cant_n$ be the -th generation in the construction of the middle-half Cantor set. The Cartesian square $\K_n = \Cant_n \times \Cant_n$ consists of squares of side-len…
L^p Estimates for Maximal Averages Along One-variable Vector Fields in R^2
Michael Bateman
We prove a conjecture of Lacey and Li in the case that the vector field depends only on one variable. Specifically: let v be a vector field defined on the unit square such that v(x…