Contents Online
Mathematical Research Letters
Volume 25 (2018)
Number 2
Sparse domination of Hilbert transforms along curves
Pages: 415 – 436
DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n2.a4
Authors
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.
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
Accepted 7 July 2017
Published 5 July 2018