Trilinear smoothing inequalities and a variant of the triangular Hilbert transform

Michael Christ, Polona Durcik, Joris Roos

Research output: Working paper

Abstract

Lebesgue space inequalities are proved for a variant of the triangular Hilbert transform involving curvature. The analysis relies on a crucial trilinear smoothing inequality developed herein, and on bounds for an anisotropic variant of the twisted paraproduct. The trilinear smoothing inequality also leads to Lebesgue space bounds for a corresponding maximal function and a quantitative nonlinear Roth-type theorem concerning patterns in the Euclidean plane.
Original languageEnglish
PublisherArXiv
Number of pages41
Publication statusPublished - 14 Nov 2020

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