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

preprint2015arXivOpen access

We are proving $L^2(\R)\times L^2(\R)\,\rightarrow\,L^1(\R)$ 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.

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

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