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) |
