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 L2 × L2 to L1 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
Milestones
Received: 13 October 2011
Accepted: 18 November 2011
Published: 1 June 2013
Authors
Xiaochun Li
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
United States