Trilinear smoothing inequalities and a variant of the triangular Hilbert transform

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.

41 pages. Expanded introduction, changed title

References in corpus (2)

• On Trilinear Oscillatory Integral Inequalities and Related Topics
• Averages of simplex Hilbert transforms

Cited by in corpus (4)

• Pointwise convergence of certain continuous-time double ergodic averages
• The non-resonant bilinear Hilbert--Carleson operator
• A strong-type Furstenberg-Sárközy theorem for sets of positive measure
• Two-point polynomial patterns in subsets of positive density in ${\mathbb{R}}^n$