$L^p$ estimates for the bilinear Hilbert transform for $1/2<p\le 2/3$: A counterexample and generalizations to non-smooth symbols

Wei Dai, Guozhen Lu

M. Lacey and C. Thiele proved in [27] (Annals of Math. (1997)) and [28] (Annals of Math. (1999)) that the bilinear Hilbert transform maps $L^{p_1}\times L^{p_2}\to L^p$ b…