%0 Journal Article
%T Single annulus $L^p$ estimates for Hilbert transforms along vector fields
%A Michael Bateman
%J Mathematics
%D 2011
%I arXiv
%X 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 $p>2$ were proved by Lacey and Li in \cite{LL1}. This paper also contains key technical ingredients for a companion paper \cite{BT} with Christoph Thiele in which $L^p$ estimates are established for the full Hilbert transform.
%U http://arxiv.org/abs/1109.6395v1