The Bilinear Hilbert-Carleson operator along the moment curve (t, t^2, t^3) satisfies the expected L^{p1} x L^{p2} to L^r bounds for 1 < p1, p2 < infinity and 1/2 < r < infinity.
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The Bilinear Hilbert-Carleson operator along curves. The purely non-zero curvature case
The Bilinear Hilbert-Carleson operator along the moment curve (t, t^2, t^3) satisfies the expected L^{p1} x L^{p2} to L^r bounds for 1 < p1, p2 < infinity and 1/2 < r < infinity.