Square functions for bi-Lipschitz maps and directional operators
Classical Analysis and ODEs
2018-08-20 v1
Abstract
First we prove a Littlewood-Paley diagonalization result for bi-Lipschitz perturbations of the identity map on the real line. This result entails a number of corollaries for the Hilbert transform along lines and monomial curves in the plane. Second, we prove a square function bound for a single scale directional operator. As a corollary we give a new proof of part of a theorem of Katz on direction fields with finitely many directions.
Cite
@article{arxiv.1706.07111,
title = {Square functions for bi-Lipschitz maps and directional operators},
author = {Francesco Di Plinio and Shaoming Guo and Christoph Thiele and Pavel Zorin-Kranich},
journal= {arXiv preprint arXiv:1706.07111},
year = {2018}
}
Comments
31 p