A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform"

2023/11/19 by Hsu, Martin, Lin, Fred Yu-Hsiang, Stokolosa, Amelia
#42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary: 42B20 #Secondary: 42B15

paper · doi:10.48550/arxiv.2311.11391

Abstract

This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard techniques in the study of oscillatory integrals with the simpler toy model of a Hilbert transform along a parabola. These standard techniques prove to be insufficient in the study of the triangular Hilbert transform with curvature. The central and novel idea in their proof of the L^p-boundedness of the triangular Hilbert transform with curvature is a trilinear smoothing inequality which we also examine in this article.

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