On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves. The Banach triangle case ($L^r,1\le r<\infty$)

Victor Lie

We show that the bilinear Hilbert transform $H_{\Gamma }$ along curves $\Gamma =(t,-\gamma (t))$ with $\gamma \in \mathcal{N}{\mathcal{F}}^C$ is bounded from $L^{p}(\mathbb{R})\times L^{q}(\mathbb{R})\,\righ…