Trilinear smoothing inequalities and a variant of the triangular Hilbert transform
Classical Analysis and ODEs
2021-08-04 v2
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.
Keywords
Cite
@article{arxiv.2008.10140,
title = {Trilinear smoothing inequalities and a variant of the triangular Hilbert transform},
author = {Michael Christ and Polona Durcik and Joris Roos},
journal= {arXiv preprint arXiv:2008.10140},
year = {2021}
}
Comments
41 pages. Expanded introduction, changed title