JournalsrmiVol. 29, No. 3pp. 1021–1069

Single annulus LpL^p estimates for Hilbert transforms along vector fields

  • Michael Bateman

    University of California Los Angeles, USA
Single annulus $L^p$ estimates for Hilbert transforms along vector fields cover

Abstract

We prove LpL^p estimates, p(1,)p\in (1,\infty), on the Hilbert transform along a one variable vector field acting on functions with frequency support in an annulus. Estimates when p>2p>2 were proved by Lacey and Li. This paper also contains key technical ingredients for a companion paper with Christoph Thiele in which LpL^p estimates are established for the full Hilbert transform. The operators considered here are singular integral variants of maximal operators arising in the study of planar differentiation problems.

Cite this article

Michael Bateman, Single annulus LpL^p estimates for Hilbert transforms along vector fields. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 1021–1069

DOI 10.4171/RMI/748