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.
Square functions for bi-Lipschitz maps and directional operators / Di Plinio, F.; Guo, S.; Thiele, C.; Zorin-Kranich, P.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 275:8(2018), pp. 2015-2058. [10.1016/j.jfa.2018.07.005]
Square functions for bi-Lipschitz maps and directional operators
Di Plinio F.
;
2018
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.File | Dimensione | Formato | |
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