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arXiv · 1109.6395

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

Michael Bateman
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Abstract

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.

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Michael Bateman. 2011-09-29. Single annulus $L^p$ estimates for Hilbert transforms along vector fields. https://arxiv.org/abs/1109.6395

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