#### Vol. 6, No. 1, 2013

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Bilinear Hilbert transforms along curves I: the monomial case

### Xiaochun Li

Vol. 6 (2013), No. 1, 197–220
##### Abstract

We establish an ${L}^{2}×{L}^{2}$ 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.

##### Keywords
bilinear Hilbert transform along curves
##### Mathematical Subject Classification 2010
Primary: 42B20, 42B25
Secondary: 46B70, 47B38