On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves

2011/10/16 by Victor Lie, Lie, Victor · 3 citations
Mathematics · #Advanced Harmonic Analysis Research #Bilinear interpolation #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Hilbert spectral analysis #Hilbert transform #Infinity #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Pure mathematics #Statistics #Zero (linguistics) #math.CA

paper · pdf · doi:10.48550/arxiv.1110.3517

published in arXiv (Cornell University) (Cornell University) · 48 pages, no figures. Published in Amer. J. Math., 137(2), pp. 313-364, 2015

openalex publication_date 2011/10/16 · arxiv created 2015/12/31 · arxiv updated 2016/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are proving L²(\R)× L²(\R) → L¹(\R) bounds for the bilinear Hilbert transform H_Γ along curves Γ=(t,-γ(t)) with γ being a smooth "non-flat" curve near zero and infinity.

Citations

• On commutators of singular integrals and bilinear singular integrals

Cited by

• On the boundedness of the curved trilinear Hilbert transform and the curved n-linear maximal operator in the quasi-Banach regime
• On Multi-linear Maximal Operators Along Homogeneous Curves
• On Polynomial Progressions Inside Sets of Large Dimension

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