A short proof on the boundedness of triangular Hilbert transform along curves
Classical Analysis and ODEs
2024-10-22 v1
Abstract
We give a short and elementary proof of the boundedness of triangular Hilbert transform along non-flat curves definable in a polynomially bounded o-minimal structure. We also provide a criterion on the multiplier to determine whether the associated fiber-wisely defined bilinear operator admits a smoothing inequality.
Cite
@article{arxiv.2410.15791,
title = {A short proof on the boundedness of triangular Hilbert transform along curves},
author = {Martin Hsu and Fred Yu-Hsiang Lin},
journal= {arXiv preprint arXiv:2410.15791},
year = {2024}
}