Mathematical Research Letters

Volume 25 (2018)

Number 2

Sparse domination of Hilbert transforms along curves

Pages: 415 – 436

DOI: http://dx.doi.org/10.4310/MRL.2018.v25.n2.a4

Authors

Laura Cladek (Department of Mathematics, University of California at Los Angeles)

Yumeng Ou (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Ma., U.S.A.)

Abstract

We obtain sharp sparse bounds for Hilbert transforms along curves in $\mathbb{R}^n$, and derive as corollaries weighted norm inequalities for such operators. The curves that we consider include monomial curves and arbitrary $C^n$ curves with nonvanishing torsion.

Keywords

sparse domination, Radon transforms, nonisotropic dilations, $L^p$-improving for curves

2010 Mathematics Subject Classification

Primary 42B20. Secondary 42B99.

Full Text (PDF format)

The authors would like to thank Michael Lacey, Francesco Di Plinio and Ioannis Parissis for helpful discussions. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester.

Received 10 May 2017

Published 5 July 2018