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

Abstract

We are proving $L^2(\mathbb{R})\times L^2(\mathbb{R})\to L^1(\mathbb{R})$ bounds for the bilinear Hilbert transform $H_{\Gamma }$ along curves $\Gamma =(t,-\gamma (t))$ with $\gamma$ being a smooth "non-flat" curve near zero and infinity.

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

Cited by in corpus (2)

• Uniform estimates for bilinear Hilbert transform and bilinear maximal functions associated to polynomials
• Bilinear Hilbert transforms associated to plane curves