English

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.

Keywords

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}
}
R2 v1 2026-06-28T19:29:21.230Z