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.
M. Christ, P. Durcik, J. Roos. Trilinear smoothing inequalities and a variant of the triangular Hilbert transform. Adv. Math. 390 (2021), 107863. https://doi.org/10.1016/j.aim.2021.107863
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.