Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896568 | Journal of Functional Analysis | 2015 | 44 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Francesco Di Plinio, Shaoming Guo, Christoph Thiele, Pavel Zorin-Kranich,