We establish an L^2 \times L^2 to L^1 estimate for the bilinear Hilbert transform along a curve defined by a monomial. Our proof is closely related to multi-linear oscillatory integrals.
New uniform bounds for a Walsh model of the bilinear Hilbert transform
Extrapolation for multilinear Muckenhoupt classes and applications to the bilinear Hilbert transform
On bilinear Hilbert transform along two polynomials
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