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arXiv · 1706.07111

Square functions for bi-Lipschitz maps and directional operators

Francesco Di Plinio·Shaoming Guo·Christoph Thiele·Pavel Zorin-Kranich
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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.

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Francesco Di Plinio, Shaoming Guo, Christoph Thiele, Pavel Zorin-Kranich. 2017-06-21. Square functions for bi-Lipschitz maps and directional operators. https://doi.org/10.1016/j.jfa.2018.07.005

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