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

Li, Xiaochun

Anal. PDE 6, No. 1, 197-220 (2013).

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