Victor Lie
Published 2011-10-16, updated 2015-12-31Version 2
We are proving $L^2(\R)\times L^2(\R)\,\rightarrow\,L^1(\R)$ 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.
Comments: 48 pages, no figures. Published in Amer. J. Math., 137(2), pp. 313-364, 2015
On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves. The Banach triangle case ($L^r,\: 1\leq r<\infty$)
The full range of uniform bounds for the bilinear Hilbert transform
Bilinear Hilbert transforms along curves I. The monomial case
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