## Bilinear Hilbert transforms along curves, I: The monomial case.(English)Zbl 1275.42022

Summary: 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 multilinear oscillatory integrals.

### MSC:

 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25 Maximal functions, Littlewood-Paley theory 46B70 Interpolation between normed linear spaces 47B38 Linear operators on function spaces (general)

### Keywords:

bilinear Hilbert transform along curves
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