M. Bateman

activity

20062011

most cited

L^{p}

estimates for the Hilbert transforms along a one-variable vector field

26 citations · 51 across the 8 of their papers we have counts for

collaborators

Showing 2011 · math.CAShow all

4 papers · 2 filters

math.CA2011★ 26 cited

$L^{p}$ 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, $L^{2}$ whenever $v$ is Lipschitz. We establish a wide range of $L^{p}$ estimates fo…

math.CA2011

Single annulus $L^{p}$ estimates for Hilbert transforms along vector fields

Michael Bateman

We prove $L^{p}$ , $p \in (1, \infty)$ estimates on the Hilbert transform along a one variable vector field acting on functions with frequency support in an annulus. Estimates when $p>2…

math.CA2011

Maximal averages along a planar vector field depending on one variable

Michael Bateman

We prove (essentially) sharp $L^{2}$ estimates for a restricted maximal operator associated to a planar vector field that depends only on the horizontal variable. The proof combines…

math.CA2011

New Bounds on cap sets

Michael Bateman, Nets Hawk Katz

We provide an improvement over Meshulam's bound on cap sets in $F_{3}^{N}$ . We show that there exist universal $ε > 0$ and $C > 0$ so that any cap set in $F_{3}^{N}$ has size at most $C {3^N \…

Lp estimates for the Hilbert transforms along a one-variable vector field

Single annulus Lp estimates for Hilbert transforms along vector fields

Maximal averages along a planar vector field depending on one variable

New Bounds on cap sets

$L^{p}$ estimates for the Hilbert transforms along a one-variable vector field

Single annulus $L^{p}$ estimates for Hilbert transforms along vector fields